Functions
Objective and constraint functions can be defined via overloaded operations
on variables and other functions. A function f
is interpreted as a
column vector, with length len(f)
and with a value that depends on
the values of its variables. Functions have two public attributes.
variables
Returns a copy of the list of variables of the function.
value
The function value. If any of the variables of f
has value
None
, then f.value()
returns None
. Otherwise,
it returns a dense 'd'
matrix of size (len(f),1)
with
the function value computed from the value
attributes of the
variables of f
.
Three types of functions are supported: affine, convex piecewise-linear,
and concave piecewise-linear.
Affine functions represent vector valued functions of the form
System Message: WARNING/2 (f(x_1,\ldots,x_n) = A_1 x_1 + \cdots + A_n x_n + b. )
latex exited with error
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L))) (/usr/share/texmf-dist/tex/generic/dehyph-exptl/dehyphn-x-2021-02-26.tex
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! I can't find file `dehypht.tex'.
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This is pdfTeX, Version 3.141592653-2.6-1.40.22 (TeX Live 2021/Mageia) (preloaded format=latex)
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The coefficients can be scalars or dense or sparse matrices. The
constant term is a scalar or a column vector.
Affine functions result from the following operations.
Unary operations For a variable x
, the unary operation +x
results in an
affine function with x
as variable, coefficient 1.0, and constant
term 0.0. The unary operation -x
returns an affine function
with x
as variable, coefficient -1.0, and constant term 0.0. For
an affine function f
, +f
is a copy of f
, and
-f
is a copy of f
with the signs of its coefficients and
constant term reversed.
Addition and subtraction Sums and differences of affine functions, variables and constants result
in new affine functions. The constant terms in the sum can be of type
integer or float, or dense or sparse 'd'
matrices with one
column.
The rules for addition and subtraction follow the conventions for
matrix addition and subtraction in the section Arithmetic Operations ,
with variables and affine functions interpreted as dense 'd'
matrices with one column. In particular, a scalar term (integer, float,
1 by 1 dense 'd'
matrix, variable of length 1, or affine
function of length 1) can be added to an affine function or variable of
length greater than 1.
Multiplication Suppose v
is an affine function or a variable, and a
is an
integer, float, sparse or dense 'd'
matrix. The products
a * v
and v * a
are valid affine functions whenever
the product is allowed under the rules for matrix and scalar
multiplication of the section Arithmetic Operations , with v
interpreted
as a 'd'
matrix with one column. In particular, the product
a * v
is defined if a
is a scalar (integer, float, or
1 by 1 dense 'd'
matrix), or a matrix (dense or sparse) with
a.size[1]
equal to len(v)
. The operation v * a
is defined if a
is scalar, or if len(v)
is 1 and a
is a
matrix with one column.
Inner products The following two functions return scalar affine functions defined
as inner products of a constant vector with a variable or affine
function.
cvxopt.modeling. sum ( v )
The argument is an affine function or a variable. The result is an
affine function of length 1, with the sum of the components of the
argument v
.
cvxopt.modeling. dot ( u , v )
If v
is a variable or affine function and u
is a
'd'
matrix of size (len(v), 1)
, then
dot(u, v)
and dot(v, u)
are equivalent to
u.trans() * v
.
If u
and v
are dense matrices, then dot
is equivalent to the function blas.dot
,
i.e., it returns the inner product of the two matrices.
In the following example, the variable x
has length 1 and y
has
length 2. The functions f
and g
are given by
System Message: WARNING/2 (f(x,y) &= \left[ \begin{array}{c} 2 \\ 2 \end{array}\right] x
+ y + \left[ \begin{array}{c} 3 \\ 3 \end{array}\right], \\
g(x,y) &=
\left[ \begin{array}{cc} 1 & 3 \\ 2 & 4 \end{array}\right] f(x,y) +
\left[ \begin{array}{cc} 1 & 1 \\ 1 & 1 \end{array} \right] y +
\left[ \begin{array}{c} 1 \\ -1 \end{array} \right] \\
&= \left[ \begin{array}{c} 8 \\ 12 \end{array}\right] x +
\left[ \begin{array}{cc} 2 & 4 \\ 3 & 5 \end{array}\right] y +
\left[ \begin{array}{c} 13 \\ 17\end{array}\right]. )
latex exited with error
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T2A Bulgarian hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-t2a.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-bg.tex
Bulgarian hyphenation patterns (options: --safe-morphology --standalone-tex, ve
rsion 21 October 2017)))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-ca.tex
EC Catalan hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-ca.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-zh-latn-pinyin.t
ex EC Pinyin Hyphenation Patterns (with tone markers) 2018-11-25 (WL)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/ptex/hyph-zh-latn-pinyin.
ec.tex)) (/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-cu.tex
No Church Slavonic hyphenation patterns - only for Unicode engines)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-cop.tex
Coptic hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex-8bit/copthyph.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-hr.tex
EC Croatian hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-hr.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-cs.tex
EC Czech hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-cs.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-da.tex
EC Danish hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-da.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-nl.tex
EC Dutch hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-nl.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-en-gb.tex
ASCII Hyphenation patterns for British English
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-en-gb.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-en-us.tex
ASCII Hyphenation patterns for American English
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-en-us.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-eo.tex
IL3 Esperanto hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-il3.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-eo.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-et.tex
EC Estonian hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-et.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-mul-ethi.tex
No Pan-Ethiopic hyphenation patterns - only for Unicode engines)
(/usr/share/texmf-dist/tex/generic/hyphen/zerohyph.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-fi.tex
EC Finnish hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-fi.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-fi-x-school.tex
EC Finnish hyphenation patterns for school
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-fi-x-school.tex)
) (/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-fr.tex
EC French hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-fr.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-fur.tex
EC Friulan hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-fur.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-gl.tex
EC Galician hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-gl.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-ka.tex
T8M Georgian hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-t8m.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-ka.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-de-1901.tex
EC German hyphenation patterns (traditional orthography)
! I can't find file `dehypht.tex'.
l.29 \input dehypht.tex
(Press Enter to retry, or Control-D to exit)
Please type another input file name:
! Emergency stop.
l.29 \input dehypht.tex
No pages of output.
Transcript written on latex.log.
mktexfmt [INFO]: log file copied to: /usr/src/.texlive2021/texmf-var/web2c/pdftex/latex.log
mktexfmt [ERROR]: running `pdftex -ini -jobname=latex -progname=latex -translate-file=cp227.tcx *latex.ini >&2 </dev/null' return status: 1
mktexfmt [ERROR]: returning error due to option --strict
mktexfmt [INFO]: disabled formats: 5
mktexfmt [INFO]: not selected formats: 53
mktexfmt [INFO]: failed to build: 1 (pdftex/latex)
mktexfmt [INFO]: total formats: 59
mktexfmt [INFO]: exiting with status 1
[stdout]
This is pdfTeX, Version 3.141592653-2.6-1.40.22 (TeX Live 2021/Mageia) (preloaded format=latex)
restricted \write18 enabled.
I can't find the format file `latex.fmt'!
>>> from cvxopt.modeling import variable
>>> x = variable ( 1 , 'x' )
>>> y = variable ( 2 , 'y' )
>>> f = 2 * x + y + 3
>>> A = matrix ([[ 1. , 2. ], [ 3. , 4. ]])
>>> b = matrix ([ 1. , - 1. ])
>>> g = A * f + sum ( y ) + b
>>> print ( g )
affine function of length 2
constant term:
[ 1.30e+01]
[ 1.70e+01]
linear term: linear function of length 2
coefficient of variable(2,'y'):
[ 2.00e+00 4.00e+00]
[ 3.00e+00 5.00e+00]
coefficient of variable(1,'x'):
[ 8.00e+00]
[ 1.20e+01]
In-place operations For an affine function f
the operations f += u
and
f -= u
, with u
a constant, a variable or an affine function,
are allowed if they do not change the length of f
, i.e., if u
has length len(f)
or length 1. In-place multiplication
f *= u
and division f /= u
are allowed if u
is an
integer, float, or 1 by 1 matrix.
Indexing and slicing Variables and affine functions admit single-argument indexing of the
four types described in the section Indexing and Slicing . The result of
an indexing or slicing operation is an affine function.
>>> x = variable ( 4 , 'x' )
>>> f = x [:: 2 ]
>>> print ( f )
linear function of length 2
linear term: linear function of length 2
coefficient of variable(4,'x'):
[ 1.00e+00 0 0 0 ]
[ 0 0 1.00e+00 0 ]
>>> y = variable ( 3 , 'x' )
>>> g = matrix ( range ( 12 ),( 3 , 4 ), 'd' ) * x - 3 * y + 1
>>> print ( g [ 0 ] + g [ 2 ])
affine function of length 1
constant term:
[ 2.00e+00]
linear term: linear function of length 1
coefficient of variable(4,'x'):
[ 2.00e+00 8.00e+00 1.40e+01 2.00e+01]
coefficient of variable(3,'x'):
[-3.00e+00 0 -3.00e+00]
The general expression of a convex piecewise-linear function is
System Message: WARNING/2 (f(x_1,\ldots,x_n) = b + A_1 x_1 + \cdots + A_n x_n +
\sum_{k=1}^K \max (y_1, y_2, \ldots, y_{m_k}). )
latex exited with error
[stderr]
kpathsea: Running mktexfmt latex.fmt
mktexfmt: mktexfmt is using the following fmtutil.cnf files (in precedence order):
mktexfmt: /usr/share/texmf-dist/web2c/fmtutil.cnf
mktexfmt: mktexfmt is using the following fmtutil.cnf file for writing changes:
mktexfmt: /usr/src/.texlive2021/texmf-config/web2c/fmtutil.cnf
mktexfmt [INFO]: writing formats under /usr/src/.texlive2021/texmf-var/web2c
mktexfmt [INFO]: --- remaking latex with pdftex
mktexfmt: running `pdftex -ini -jobname=latex -progname=latex -translate-file=cp227.tcx *latex.ini' ...
This is pdfTeX, Version 3.141592653-2.6-1.40.22 (TeX Live 2021/Mageia) (INITEX)
restricted \write18 enabled.
(/usr/share/texmf-dist/web2c/cp227.tcx)
entering extended mode
(/usr/share/texmf-dist/tex/latex/latexconfig/latex.ini
(/usr/share/texmf-dist/tex/generic/config/pdftexconfig.tex)
(/usr/share/texmf-dist/tex/latex/base/latex.ltx
(/usr/share/texmf-dist/tex/latex/base/texsys.cfg)
./texsys.aux found
\@currdir set to: ./.
Assuming \openin and \input
have the same search path.
Defining UNIX/DOS style filename parser.
catcodes, registers, parameters,
LaTeX2e <2020-10-01> patch level 4
(/usr/share/texmf-dist/tex/latex/l3kernel/expl3.ltx
(/usr/share/texmf-dist/tex/latex/l3kernel/expl3-code.tex
! LaTeX3 Error: File 'UnicodeData.txt' not found.
For immediate help type H <return>.
...
l.30209 }
(/usr/share/texmf-dist/tex/latex/l3kernel/l3deprecation.def)))
(/usr/share/texmf-dist/tex/latex/l3packages/xparse/xparse.ltx
(/usr/share/texmf-dist/tex/latex/l3packages/xparse/xparse-generic.tex)) hacks,
control, par, spacing, files, font encodings, lengths,
====================================
Local config file fonttext.cfg used
====================================
(/usr/share/texmf-dist/tex/latex/base/fonttext.cfg
(/usr/share/texmf-dist/tex/latex/base/fonttext.ltx
=== Don't modify this file, use a .cfg file instead ===
(/usr/share/texmf-dist/tex/latex/base/omlenc.def)
(/usr/share/texmf-dist/tex/latex/base/omsenc.def)
(/usr/share/texmf-dist/tex/latex/base/ot1enc.def)
(/usr/share/texmf-dist/tex/latex/base/t1enc.def)
(/usr/share/texmf-dist/tex/latex/base/ts1enc.def)
(/usr/share/texmf-dist/tex/latex/base/ts1cmr.fd)
(/usr/share/texmf-dist/tex/latex/base/t1cmr.fd)
(/usr/share/texmf-dist/tex/latex/base/ot1cmr.fd)
(/usr/share/texmf-dist/tex/latex/base/ot1cmss.fd)
(/usr/share/texmf-dist/tex/latex/base/ot1cmtt.fd)))
====================================
Local config file fontmath.cfg used
====================================
(/usr/share/texmf-dist/tex/latex/base/fontmath.cfg
(/usr/share/texmf-dist/tex/latex/base/fontmath.ltx
=== Don't modify this file, use a .cfg file instead ===
(/usr/share/texmf-dist/tex/latex/base/omlcmm.fd)
(/usr/share/texmf-dist/tex/latex/base/omscmsy.fd)
(/usr/share/texmf-dist/tex/latex/base/omxcmex.fd)
(/usr/share/texmf-dist/tex/latex/base/ucmr.fd)))
====================================
Local config file preload.cfg used
=====================================
(/usr/share/texmf-dist/tex/latex/base/preload.cfg
(/usr/share/texmf-dist/tex/latex/base/preload.ltx)) page nos., x-ref,
environments, center, verbatim, math definitions, boxes, title, sectioning,
contents, floats, footnotes, index, bibliography, output,
===========================================
Local configuration file hyphen.cfg used
===========================================
(/usr/share/texmf-dist/tex/generic/babel/hyphen.cfg
(/usr/share/texmf-dist/tex/generic/hyphen/hyphen.tex)
(/usr/share/texmf-dist/tex/generic/hyphen/dumyhyph.tex)
(/usr/share/texmf-dist/tex/generic/hyphen/zerohyph.tex)
(/usr/share/texmf-dist/tex/generic/dehyph-exptl/dehypht-x-2021-02-26.tex
dehyph-exptl: using an 8-bit TeX engine.
(/usr/share/texmf-dist/tex/generic/dehyph-exptl/dehypht-x-2021-02-26.pat
German Hyphenation Patterns (Traditional Orthography) `dehypht-x' 2021-02-26 (W
L))) (/usr/share/texmf-dist/tex/generic/dehyph-exptl/dehyphn-x-2021-02-26.tex
dehyph-exptl: using an 8-bit TeX engine.
(/usr/share/texmf-dist/tex/generic/dehyph-exptl/dehyphn-x-2021-02-26.pat
German Hyphenation Patterns (Reformed Orthography, 2006) `dehyphn-x' 2021-02-26
(WL))) (/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-af.tex
EC Afrikaans hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-af.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-grc.tex
Hyphenation patterns for Ancient Greek
(/usr/share/texmf-dist/tex/generic/hyphen/grahyph5.tex
Hyphenation patterns for Ancient Greek))
(/usr/share/texmf-dist/tex/generic/hyphen/ibyhyph.tex
Greek hyphenation patterns for Ibycus encoding, v3.0)
(/usr/share/texmf-dist/tex/generic/hyphen/zerohyph.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-hy.tex
No Armenian hyphenation patterns - only for Unicode engines)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-eu.tex
EC Basque hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-eu.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-be.tex
T2A Belarusian hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-t2a.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-be.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-bg.tex
T2A Bulgarian hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-t2a.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-bg.tex
Bulgarian hyphenation patterns (options: --safe-morphology --standalone-tex, ve
rsion 21 October 2017)))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-ca.tex
EC Catalan hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-ca.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-zh-latn-pinyin.t
ex EC Pinyin Hyphenation Patterns (with tone markers) 2018-11-25 (WL)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/ptex/hyph-zh-latn-pinyin.
ec.tex)) (/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-cu.tex
No Church Slavonic hyphenation patterns - only for Unicode engines)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-cop.tex
Coptic hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex-8bit/copthyph.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-hr.tex
EC Croatian hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-hr.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-cs.tex
EC Czech hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-cs.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-da.tex
EC Danish hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-da.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-nl.tex
EC Dutch hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-nl.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-en-gb.tex
ASCII Hyphenation patterns for British English
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-en-gb.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-en-us.tex
ASCII Hyphenation patterns for American English
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-en-us.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-eo.tex
IL3 Esperanto hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-il3.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-eo.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-et.tex
EC Estonian hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-et.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-mul-ethi.tex
No Pan-Ethiopic hyphenation patterns - only for Unicode engines)
(/usr/share/texmf-dist/tex/generic/hyphen/zerohyph.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-fi.tex
EC Finnish hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-fi.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-fi-x-school.tex
EC Finnish hyphenation patterns for school
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-fi-x-school.tex)
) (/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-fr.tex
EC French hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-fr.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-fur.tex
EC Friulan hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-fur.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-gl.tex
EC Galician hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-gl.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-ka.tex
T8M Georgian hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-t8m.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-ka.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-de-1901.tex
EC German hyphenation patterns (traditional orthography)
! I can't find file `dehypht.tex'.
l.29 \input dehypht.tex
(Press Enter to retry, or Control-D to exit)
Please type another input file name:
! Emergency stop.
l.29 \input dehypht.tex
No pages of output.
Transcript written on latex.log.
mktexfmt [INFO]: log file copied to: /usr/src/.texlive2021/texmf-var/web2c/pdftex/latex.log
mktexfmt [ERROR]: running `pdftex -ini -jobname=latex -progname=latex -translate-file=cp227.tcx *latex.ini >&2 </dev/null' return status: 1
mktexfmt [ERROR]: returning error due to option --strict
mktexfmt [INFO]: disabled formats: 5
mktexfmt [INFO]: not selected formats: 53
mktexfmt [INFO]: failed to build: 1 (pdftex/latex)
mktexfmt [INFO]: total formats: 59
mktexfmt [INFO]: exiting with status 1
[stdout]
This is pdfTeX, Version 3.141592653-2.6-1.40.22 (TeX Live 2021/Mageia) (preloaded format=latex)
restricted \write18 enabled.
I can't find the format file `latex.fmt'!
The maximum in this expression is a componentwise maximum of its vector
arguments, which can be constant vectors, variables, affine functions or
convex piecewise-linear functions. The general expression for a
concave piecewise-linear function is
System Message: WARNING/2 (f(x_1,\ldots,x_n) = b + A_1 x_1 + \cdots + A_n x_n +
\sum_{k=1}^K \min (y_1, y_2, \ldots, y_{m_k}). )
latex exited with error
[stderr]
kpathsea: Running mktexfmt latex.fmt
mktexfmt: mktexfmt is using the following fmtutil.cnf files (in precedence order):
mktexfmt: /usr/share/texmf-dist/web2c/fmtutil.cnf
mktexfmt: mktexfmt is using the following fmtutil.cnf file for writing changes:
mktexfmt: /usr/src/.texlive2021/texmf-config/web2c/fmtutil.cnf
mktexfmt [INFO]: writing formats under /usr/src/.texlive2021/texmf-var/web2c
mktexfmt [INFO]: --- remaking latex with pdftex
mktexfmt: running `pdftex -ini -jobname=latex -progname=latex -translate-file=cp227.tcx *latex.ini' ...
This is pdfTeX, Version 3.141592653-2.6-1.40.22 (TeX Live 2021/Mageia) (INITEX)
restricted \write18 enabled.
(/usr/share/texmf-dist/web2c/cp227.tcx)
entering extended mode
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l.30209 }
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(/usr/share/texmf-dist/tex/latex/l3packages/xparse/xparse.ltx
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====================================
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====================================
(/usr/share/texmf-dist/tex/latex/base/fonttext.cfg
(/usr/share/texmf-dist/tex/latex/base/fonttext.ltx
=== Don't modify this file, use a .cfg file instead ===
(/usr/share/texmf-dist/tex/latex/base/omlenc.def)
(/usr/share/texmf-dist/tex/latex/base/omsenc.def)
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(/usr/share/texmf-dist/tex/latex/base/t1enc.def)
(/usr/share/texmf-dist/tex/latex/base/ts1enc.def)
(/usr/share/texmf-dist/tex/latex/base/ts1cmr.fd)
(/usr/share/texmf-dist/tex/latex/base/t1cmr.fd)
(/usr/share/texmf-dist/tex/latex/base/ot1cmr.fd)
(/usr/share/texmf-dist/tex/latex/base/ot1cmss.fd)
(/usr/share/texmf-dist/tex/latex/base/ot1cmtt.fd)))
====================================
Local config file fontmath.cfg used
====================================
(/usr/share/texmf-dist/tex/latex/base/fontmath.cfg
(/usr/share/texmf-dist/tex/latex/base/fontmath.ltx
=== Don't modify this file, use a .cfg file instead ===
(/usr/share/texmf-dist/tex/latex/base/omlcmm.fd)
(/usr/share/texmf-dist/tex/latex/base/omscmsy.fd)
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====================================
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===========================================
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(/usr/share/texmf-dist/tex/generic/hyphen/hyphen.tex)
(/usr/share/texmf-dist/tex/generic/hyphen/dumyhyph.tex)
(/usr/share/texmf-dist/tex/generic/hyphen/zerohyph.tex)
(/usr/share/texmf-dist/tex/generic/dehyph-exptl/dehypht-x-2021-02-26.tex
dehyph-exptl: using an 8-bit TeX engine.
(/usr/share/texmf-dist/tex/generic/dehyph-exptl/dehypht-x-2021-02-26.pat
German Hyphenation Patterns (Traditional Orthography) `dehypht-x' 2021-02-26 (W
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dehyph-exptl: using an 8-bit TeX engine.
(/usr/share/texmf-dist/tex/generic/dehyph-exptl/dehyphn-x-2021-02-26.pat
German Hyphenation Patterns (Reformed Orthography, 2006) `dehyphn-x' 2021-02-26
(WL))) (/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-af.tex
EC Afrikaans hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-af.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-grc.tex
Hyphenation patterns for Ancient Greek
(/usr/share/texmf-dist/tex/generic/hyphen/grahyph5.tex
Hyphenation patterns for Ancient Greek))
(/usr/share/texmf-dist/tex/generic/hyphen/ibyhyph.tex
Greek hyphenation patterns for Ibycus encoding, v3.0)
(/usr/share/texmf-dist/tex/generic/hyphen/zerohyph.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-hy.tex
No Armenian hyphenation patterns - only for Unicode engines)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-eu.tex
EC Basque hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-eu.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-be.tex
T2A Belarusian hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-t2a.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-be.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-bg.tex
T2A Bulgarian hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-t2a.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-bg.tex
Bulgarian hyphenation patterns (options: --safe-morphology --standalone-tex, ve
rsion 21 October 2017)))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-ca.tex
EC Catalan hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-ca.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-zh-latn-pinyin.t
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(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/ptex/hyph-zh-latn-pinyin.
ec.tex)) (/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-cu.tex
No Church Slavonic hyphenation patterns - only for Unicode engines)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-cop.tex
Coptic hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex-8bit/copthyph.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-hr.tex
EC Croatian hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-hr.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-cs.tex
EC Czech hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-cs.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-da.tex
EC Danish hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-da.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-nl.tex
EC Dutch hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-nl.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-en-gb.tex
ASCII Hyphenation patterns for British English
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-en-gb.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-en-us.tex
ASCII Hyphenation patterns for American English
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-en-us.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-eo.tex
IL3 Esperanto hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-il3.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-eo.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-et.tex
EC Estonian hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-et.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-mul-ethi.tex
No Pan-Ethiopic hyphenation patterns - only for Unicode engines)
(/usr/share/texmf-dist/tex/generic/hyphen/zerohyph.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-fi.tex
EC Finnish hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-fi.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-fi-x-school.tex
EC Finnish hyphenation patterns for school
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-fi-x-school.tex)
) (/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-fr.tex
EC French hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-fr.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-fur.tex
EC Friulan hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-fur.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-gl.tex
EC Galician hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-gl.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-ka.tex
T8M Georgian hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-t8m.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-ka.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-de-1901.tex
EC German hyphenation patterns (traditional orthography)
! I can't find file `dehypht.tex'.
l.29 \input dehypht.tex
(Press Enter to retry, or Control-D to exit)
Please type another input file name:
! Emergency stop.
l.29 \input dehypht.tex
No pages of output.
Transcript written on latex.log.
mktexfmt [INFO]: log file copied to: /usr/src/.texlive2021/texmf-var/web2c/pdftex/latex.log
mktexfmt [ERROR]: running `pdftex -ini -jobname=latex -progname=latex -translate-file=cp227.tcx *latex.ini >&2 </dev/null' return status: 1
mktexfmt [ERROR]: returning error due to option --strict
mktexfmt [INFO]: disabled formats: 5
mktexfmt [INFO]: not selected formats: 53
mktexfmt [INFO]: failed to build: 1 (pdftex/latex)
mktexfmt [INFO]: total formats: 59
mktexfmt [INFO]: exiting with status 1
[stdout]
This is pdfTeX, Version 3.141592653-2.6-1.40.22 (TeX Live 2021/Mageia) (preloaded format=latex)
restricted \write18 enabled.
I can't find the format file `latex.fmt'!
Here the arguments of the min
can be constants, variables, affine
functions or concave piecewise-linear functions.
Piecewise-linear functions can be created using the following
operations.
Maximum If the arguments in f = max(y1, y2, ...)
do not include any
variables or functions, then the Python built-in max
is
evaluated.
If one or more of the arguments are variables or functions,
max
returns a piecewise-linear function defined as the elementwise maximum
of its arguments. In other words,
f[k] = max(y1[k], y2[k], ...)
for k
= 0, …,
len(f) - 1
. The length of f
is equal to the maximum of the
lengths of the arguments. Each argument must have length equal to
len(f)
or length one. Arguments with length one are interpreted
as vectors of length len(f)
with identical entries.
The arguments can be scalars of type integer or float, dense
'd'
matrices with one column, variables, affine functions or
convex piecewise-linear functions.
With one argument, f = max(u)
is interpreted as
f = max(u[0], u[1], ..., u[len(u)-1])
.
Minimum Similar to max
but returns a concave piecewise-linear
function.
The arguments can be scalars of type integer or float, dense
'd'
matrices with one column, variables, affine functions or
concave piecewise-linear functions.
Absolute value If u
is a variable or affine function then f = abs(u)
returns the convex piecewise-linear function max(u, -u)
.
Unary plus and minus +f
creates a copy of f
. -f
is a concave
piecewise-linear function if f
is convex and a convex
piecewise-linear function if f
is concave.
Addition and subtraction Sums and differences involving piecewise-linear functions are allowed
if they result in convex or concave functions. For example, one can add
two convex or two concave functions, but not a convex and a concave
function. The command sum(f)
is equivalent to
f[0] + f[1] + ... + f[len(f) - 1]
.
Multiplication Scalar multiplication a * f
of a piecewise-linear function f
is defined if a
is an integer, float, 1 by 1 'd'
matrix.
Matrix-matrix multiplications a * f
or f * a
are only
defined if a
is a dense or sparse 1 by 1 matrix.
Indexing and slicing Piecewise-linear functions admit single-argument indexing of the four
types described in the section Indexing and Slicing . The result of an
indexing or slicing operation is a new piecewise-linear function.
In the following example, f
is the 1-norm of a vector variable x
of
length 10, g
is its infinity-norm, and h
is the function
System Message: WARNING/2 (h(x) = \sum_k \phi(x[k]), \qquad
\phi(u) = \left\{\begin{array}{ll}
0 & |u| \leq 1 \\
|u|-1 & 1 \leq |u| \leq 2 \\
2|u|-3 & |u| \geq 2.
\end{array}\right. )
latex exited with error
[stderr]
kpathsea: Running mktexfmt latex.fmt
mktexfmt: mktexfmt is using the following fmtutil.cnf files (in precedence order):
mktexfmt: /usr/share/texmf-dist/web2c/fmtutil.cnf
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mktexfmt [INFO]: writing formats under /usr/src/.texlive2021/texmf-var/web2c
mktexfmt [INFO]: --- remaking latex with pdftex
mktexfmt: running `pdftex -ini -jobname=latex -progname=latex -translate-file=cp227.tcx *latex.ini' ...
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./texsys.aux found
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Assuming \openin and \input
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LaTeX2e <2020-10-01> patch level 4
(/usr/share/texmf-dist/tex/latex/l3kernel/expl3.ltx
(/usr/share/texmf-dist/tex/latex/l3kernel/expl3-code.tex
! LaTeX3 Error: File 'UnicodeData.txt' not found.
For immediate help type H <return>.
...
l.30209 }
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(/usr/share/texmf-dist/tex/latex/l3packages/xparse/xparse.ltx
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====================================
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====================================
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(/usr/share/texmf-dist/tex/latex/base/ot1cmtt.fd)))
====================================
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====================================
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(/usr/share/texmf-dist/tex/latex/base/fontmath.ltx
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====================================
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=====================================
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(/usr/share/texmf-dist/tex/latex/base/preload.ltx)) page nos., x-ref,
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===========================================
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(/usr/share/texmf-dist/tex/generic/hyphen/hyphen.tex)
(/usr/share/texmf-dist/tex/generic/hyphen/dumyhyph.tex)
(/usr/share/texmf-dist/tex/generic/hyphen/zerohyph.tex)
(/usr/share/texmf-dist/tex/generic/dehyph-exptl/dehypht-x-2021-02-26.tex
dehyph-exptl: using an 8-bit TeX engine.
(/usr/share/texmf-dist/tex/generic/dehyph-exptl/dehypht-x-2021-02-26.pat
German Hyphenation Patterns (Traditional Orthography) `dehypht-x' 2021-02-26 (W
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dehyph-exptl: using an 8-bit TeX engine.
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German Hyphenation Patterns (Reformed Orthography, 2006) `dehyphn-x' 2021-02-26
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EC Afrikaans hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-af.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-grc.tex
Hyphenation patterns for Ancient Greek
(/usr/share/texmf-dist/tex/generic/hyphen/grahyph5.tex
Hyphenation patterns for Ancient Greek))
(/usr/share/texmf-dist/tex/generic/hyphen/ibyhyph.tex
Greek hyphenation patterns for Ibycus encoding, v3.0)
(/usr/share/texmf-dist/tex/generic/hyphen/zerohyph.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-hy.tex
No Armenian hyphenation patterns - only for Unicode engines)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-eu.tex
EC Basque hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-eu.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-be.tex
T2A Belarusian hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-t2a.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-be.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-bg.tex
T2A Bulgarian hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-t2a.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-bg.tex
Bulgarian hyphenation patterns (options: --safe-morphology --standalone-tex, ve
rsion 21 October 2017)))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-ca.tex
EC Catalan hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-ca.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-zh-latn-pinyin.t
ex EC Pinyin Hyphenation Patterns (with tone markers) 2018-11-25 (WL)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/ptex/hyph-zh-latn-pinyin.
ec.tex)) (/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-cu.tex
No Church Slavonic hyphenation patterns - only for Unicode engines)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-cop.tex
Coptic hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex-8bit/copthyph.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-hr.tex
EC Croatian hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-hr.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-cs.tex
EC Czech hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-cs.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-da.tex
EC Danish hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-da.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-nl.tex
EC Dutch hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-nl.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-en-gb.tex
ASCII Hyphenation patterns for British English
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-en-gb.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-en-us.tex
ASCII Hyphenation patterns for American English
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-en-us.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-eo.tex
IL3 Esperanto hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-il3.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-eo.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-et.tex
EC Estonian hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-et.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-mul-ethi.tex
No Pan-Ethiopic hyphenation patterns - only for Unicode engines)
(/usr/share/texmf-dist/tex/generic/hyphen/zerohyph.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-fi.tex
EC Finnish hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-fi.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-fi-x-school.tex
EC Finnish hyphenation patterns for school
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-fi-x-school.tex)
) (/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-fr.tex
EC French hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-fr.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-fur.tex
EC Friulan hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-fur.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-gl.tex
EC Galician hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-gl.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-ka.tex
T8M Georgian hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-t8m.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-ka.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-de-1901.tex
EC German hyphenation patterns (traditional orthography)
! I can't find file `dehypht.tex'.
l.29 \input dehypht.tex
(Press Enter to retry, or Control-D to exit)
Please type another input file name:
! Emergency stop.
l.29 \input dehypht.tex
No pages of output.
Transcript written on latex.log.
mktexfmt [INFO]: log file copied to: /usr/src/.texlive2021/texmf-var/web2c/pdftex/latex.log
mktexfmt [ERROR]: running `pdftex -ini -jobname=latex -progname=latex -translate-file=cp227.tcx *latex.ini >&2 </dev/null' return status: 1
mktexfmt [ERROR]: returning error due to option --strict
mktexfmt [INFO]: disabled formats: 5
mktexfmt [INFO]: not selected formats: 53
mktexfmt [INFO]: failed to build: 1 (pdftex/latex)
mktexfmt [INFO]: total formats: 59
mktexfmt [INFO]: exiting with status 1
[stdout]
This is pdfTeX, Version 3.141592653-2.6-1.40.22 (TeX Live 2021/Mageia) (preloaded format=latex)
restricted \write18 enabled.
I can't find the format file `latex.fmt'!
>>> from cvxopt.modeling import variable , max
>>> x = variable ( 10 , 'x' )
>>> f = sum ( abs ( x ))
>>> g = max ( abs ( x ))
>>> h = sum ( max ( 0 , abs ( x ) - 1 , 2 * abs ( x ) - 3 ))
In-place operations If f
is piecewise-linear then the in-place operations
f += u
, f -= u
, f *= u
, f /= u
are
defined if the corresponding expanded operations f = f + u
,
f = f - u
, f = f * u
, and f = f/u
are defined
and if they do not change the length of f
.
Constraints
Linear equality and inequality constraints of the form
System Message: WARNING/2 (f(x_1,\ldots,x_n) = 0, \qquad f(x_1,\ldots,x_n) \preceq 0, )
latex exited with error
[stderr]
kpathsea: Running mktexfmt latex.fmt
mktexfmt: mktexfmt is using the following fmtutil.cnf files (in precedence order):
mktexfmt: /usr/share/texmf-dist/web2c/fmtutil.cnf
mktexfmt: mktexfmt is using the following fmtutil.cnf file for writing changes:
mktexfmt: /usr/src/.texlive2021/texmf-config/web2c/fmtutil.cnf
mktexfmt [INFO]: writing formats under /usr/src/.texlive2021/texmf-var/web2c
mktexfmt [INFO]: --- remaking latex with pdftex
mktexfmt: running `pdftex -ini -jobname=latex -progname=latex -translate-file=cp227.tcx *latex.ini' ...
This is pdfTeX, Version 3.141592653-2.6-1.40.22 (TeX Live 2021/Mageia) (INITEX)
restricted \write18 enabled.
(/usr/share/texmf-dist/web2c/cp227.tcx)
entering extended mode
(/usr/share/texmf-dist/tex/latex/latexconfig/latex.ini
(/usr/share/texmf-dist/tex/generic/config/pdftexconfig.tex)
(/usr/share/texmf-dist/tex/latex/base/latex.ltx
(/usr/share/texmf-dist/tex/latex/base/texsys.cfg)
./texsys.aux found
\@currdir set to: ./.
Assuming \openin and \input
have the same search path.
Defining UNIX/DOS style filename parser.
catcodes, registers, parameters,
LaTeX2e <2020-10-01> patch level 4
(/usr/share/texmf-dist/tex/latex/l3kernel/expl3.ltx
(/usr/share/texmf-dist/tex/latex/l3kernel/expl3-code.tex
! LaTeX3 Error: File 'UnicodeData.txt' not found.
For immediate help type H <return>.
...
l.30209 }
(/usr/share/texmf-dist/tex/latex/l3kernel/l3deprecation.def)))
(/usr/share/texmf-dist/tex/latex/l3packages/xparse/xparse.ltx
(/usr/share/texmf-dist/tex/latex/l3packages/xparse/xparse-generic.tex)) hacks,
control, par, spacing, files, font encodings, lengths,
====================================
Local config file fonttext.cfg used
====================================
(/usr/share/texmf-dist/tex/latex/base/fonttext.cfg
(/usr/share/texmf-dist/tex/latex/base/fonttext.ltx
=== Don't modify this file, use a .cfg file instead ===
(/usr/share/texmf-dist/tex/latex/base/omlenc.def)
(/usr/share/texmf-dist/tex/latex/base/omsenc.def)
(/usr/share/texmf-dist/tex/latex/base/ot1enc.def)
(/usr/share/texmf-dist/tex/latex/base/t1enc.def)
(/usr/share/texmf-dist/tex/latex/base/ts1enc.def)
(/usr/share/texmf-dist/tex/latex/base/ts1cmr.fd)
(/usr/share/texmf-dist/tex/latex/base/t1cmr.fd)
(/usr/share/texmf-dist/tex/latex/base/ot1cmr.fd)
(/usr/share/texmf-dist/tex/latex/base/ot1cmss.fd)
(/usr/share/texmf-dist/tex/latex/base/ot1cmtt.fd)))
====================================
Local config file fontmath.cfg used
====================================
(/usr/share/texmf-dist/tex/latex/base/fontmath.cfg
(/usr/share/texmf-dist/tex/latex/base/fontmath.ltx
=== Don't modify this file, use a .cfg file instead ===
(/usr/share/texmf-dist/tex/latex/base/omlcmm.fd)
(/usr/share/texmf-dist/tex/latex/base/omscmsy.fd)
(/usr/share/texmf-dist/tex/latex/base/omxcmex.fd)
(/usr/share/texmf-dist/tex/latex/base/ucmr.fd)))
====================================
Local config file preload.cfg used
=====================================
(/usr/share/texmf-dist/tex/latex/base/preload.cfg
(/usr/share/texmf-dist/tex/latex/base/preload.ltx)) page nos., x-ref,
environments, center, verbatim, math definitions, boxes, title, sectioning,
contents, floats, footnotes, index, bibliography, output,
===========================================
Local configuration file hyphen.cfg used
===========================================
(/usr/share/texmf-dist/tex/generic/babel/hyphen.cfg
(/usr/share/texmf-dist/tex/generic/hyphen/hyphen.tex)
(/usr/share/texmf-dist/tex/generic/hyphen/dumyhyph.tex)
(/usr/share/texmf-dist/tex/generic/hyphen/zerohyph.tex)
(/usr/share/texmf-dist/tex/generic/dehyph-exptl/dehypht-x-2021-02-26.tex
dehyph-exptl: using an 8-bit TeX engine.
(/usr/share/texmf-dist/tex/generic/dehyph-exptl/dehypht-x-2021-02-26.pat
German Hyphenation Patterns (Traditional Orthography) `dehypht-x' 2021-02-26 (W
L))) (/usr/share/texmf-dist/tex/generic/dehyph-exptl/dehyphn-x-2021-02-26.tex
dehyph-exptl: using an 8-bit TeX engine.
(/usr/share/texmf-dist/tex/generic/dehyph-exptl/dehyphn-x-2021-02-26.pat
German Hyphenation Patterns (Reformed Orthography, 2006) `dehyphn-x' 2021-02-26
(WL))) (/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-af.tex
EC Afrikaans hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-af.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-grc.tex
Hyphenation patterns for Ancient Greek
(/usr/share/texmf-dist/tex/generic/hyphen/grahyph5.tex
Hyphenation patterns for Ancient Greek))
(/usr/share/texmf-dist/tex/generic/hyphen/ibyhyph.tex
Greek hyphenation patterns for Ibycus encoding, v3.0)
(/usr/share/texmf-dist/tex/generic/hyphen/zerohyph.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-hy.tex
No Armenian hyphenation patterns - only for Unicode engines)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-eu.tex
EC Basque hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-eu.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-be.tex
T2A Belarusian hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-t2a.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-be.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-bg.tex
T2A Bulgarian hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-t2a.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-bg.tex
Bulgarian hyphenation patterns (options: --safe-morphology --standalone-tex, ve
rsion 21 October 2017)))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-ca.tex
EC Catalan hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-ca.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-zh-latn-pinyin.t
ex EC Pinyin Hyphenation Patterns (with tone markers) 2018-11-25 (WL)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/ptex/hyph-zh-latn-pinyin.
ec.tex)) (/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-cu.tex
No Church Slavonic hyphenation patterns - only for Unicode engines)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-cop.tex
Coptic hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex-8bit/copthyph.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-hr.tex
EC Croatian hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-hr.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-cs.tex
EC Czech hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-cs.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-da.tex
EC Danish hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-da.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-nl.tex
EC Dutch hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-nl.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-en-gb.tex
ASCII Hyphenation patterns for British English
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-en-gb.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-en-us.tex
ASCII Hyphenation patterns for American English
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-en-us.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-eo.tex
IL3 Esperanto hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-il3.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-eo.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-et.tex
EC Estonian hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-et.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-mul-ethi.tex
No Pan-Ethiopic hyphenation patterns - only for Unicode engines)
(/usr/share/texmf-dist/tex/generic/hyphen/zerohyph.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-fi.tex
EC Finnish hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-fi.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-fi-x-school.tex
EC Finnish hyphenation patterns for school
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-fi-x-school.tex)
) (/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-fr.tex
EC French hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-fr.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-fur.tex
EC Friulan hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-fur.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-gl.tex
EC Galician hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-gl.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-ka.tex
T8M Georgian hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-t8m.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-ka.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-de-1901.tex
EC German hyphenation patterns (traditional orthography)
! I can't find file `dehypht.tex'.
l.29 \input dehypht.tex
(Press Enter to retry, or Control-D to exit)
Please type another input file name:
! Emergency stop.
l.29 \input dehypht.tex
No pages of output.
Transcript written on latex.log.
mktexfmt [INFO]: log file copied to: /usr/src/.texlive2021/texmf-var/web2c/pdftex/latex.log
mktexfmt [ERROR]: running `pdftex -ini -jobname=latex -progname=latex -translate-file=cp227.tcx *latex.ini >&2 </dev/null' return status: 1
mktexfmt [ERROR]: returning error due to option --strict
mktexfmt [INFO]: disabled formats: 5
mktexfmt [INFO]: not selected formats: 53
mktexfmt [INFO]: failed to build: 1 (pdftex/latex)
mktexfmt [INFO]: total formats: 59
mktexfmt [INFO]: exiting with status 1
[stdout]
This is pdfTeX, Version 3.141592653-2.6-1.40.22 (TeX Live 2021/Mageia) (preloaded format=latex)
restricted \write18 enabled.
I can't find the format file `latex.fmt'!
where
System Message: WARNING/2 (f )
latex exited with error
[stderr]
kpathsea: Running mktexfmt latex.fmt
mktexfmt: mktexfmt is using the following fmtutil.cnf files (in precedence order):
mktexfmt: /usr/share/texmf-dist/web2c/fmtutil.cnf
mktexfmt: mktexfmt is using the following fmtutil.cnf file for writing changes:
mktexfmt: /usr/src/.texlive2021/texmf-config/web2c/fmtutil.cnf
mktexfmt [INFO]: writing formats under /usr/src/.texlive2021/texmf-var/web2c
mktexfmt [INFO]: --- remaking latex with pdftex
mktexfmt: running `pdftex -ini -jobname=latex -progname=latex -translate-file=cp227.tcx *latex.ini' ...
This is pdfTeX, Version 3.141592653-2.6-1.40.22 (TeX Live 2021/Mageia) (INITEX)
restricted \write18 enabled.
(/usr/share/texmf-dist/web2c/cp227.tcx)
entering extended mode
(/usr/share/texmf-dist/tex/latex/latexconfig/latex.ini
(/usr/share/texmf-dist/tex/generic/config/pdftexconfig.tex)
(/usr/share/texmf-dist/tex/latex/base/latex.ltx
(/usr/share/texmf-dist/tex/latex/base/texsys.cfg)
./texsys.aux found
\@currdir set to: ./.
Assuming \openin and \input
have the same search path.
Defining UNIX/DOS style filename parser.
catcodes, registers, parameters,
LaTeX2e <2020-10-01> patch level 4
(/usr/share/texmf-dist/tex/latex/l3kernel/expl3.ltx
(/usr/share/texmf-dist/tex/latex/l3kernel/expl3-code.tex
! LaTeX3 Error: File 'UnicodeData.txt' not found.
For immediate help type H <return>.
...
l.30209 }
(/usr/share/texmf-dist/tex/latex/l3kernel/l3deprecation.def)))
(/usr/share/texmf-dist/tex/latex/l3packages/xparse/xparse.ltx
(/usr/share/texmf-dist/tex/latex/l3packages/xparse/xparse-generic.tex)) hacks,
control, par, spacing, files, font encodings, lengths,
====================================
Local config file fonttext.cfg used
====================================
(/usr/share/texmf-dist/tex/latex/base/fonttext.cfg
(/usr/share/texmf-dist/tex/latex/base/fonttext.ltx
=== Don't modify this file, use a .cfg file instead ===
(/usr/share/texmf-dist/tex/latex/base/omlenc.def)
(/usr/share/texmf-dist/tex/latex/base/omsenc.def)
(/usr/share/texmf-dist/tex/latex/base/ot1enc.def)
(/usr/share/texmf-dist/tex/latex/base/t1enc.def)
(/usr/share/texmf-dist/tex/latex/base/ts1enc.def)
(/usr/share/texmf-dist/tex/latex/base/ts1cmr.fd)
(/usr/share/texmf-dist/tex/latex/base/t1cmr.fd)
(/usr/share/texmf-dist/tex/latex/base/ot1cmr.fd)
(/usr/share/texmf-dist/tex/latex/base/ot1cmss.fd)
(/usr/share/texmf-dist/tex/latex/base/ot1cmtt.fd)))
====================================
Local config file fontmath.cfg used
====================================
(/usr/share/texmf-dist/tex/latex/base/fontmath.cfg
(/usr/share/texmf-dist/tex/latex/base/fontmath.ltx
=== Don't modify this file, use a .cfg file instead ===
(/usr/share/texmf-dist/tex/latex/base/omlcmm.fd)
(/usr/share/texmf-dist/tex/latex/base/omscmsy.fd)
(/usr/share/texmf-dist/tex/latex/base/omxcmex.fd)
(/usr/share/texmf-dist/tex/latex/base/ucmr.fd)))
====================================
Local config file preload.cfg used
=====================================
(/usr/share/texmf-dist/tex/latex/base/preload.cfg
(/usr/share/texmf-dist/tex/latex/base/preload.ltx)) page nos., x-ref,
environments, center, verbatim, math definitions, boxes, title, sectioning,
contents, floats, footnotes, index, bibliography, output,
===========================================
Local configuration file hyphen.cfg used
===========================================
(/usr/share/texmf-dist/tex/generic/babel/hyphen.cfg
(/usr/share/texmf-dist/tex/generic/hyphen/hyphen.tex)
(/usr/share/texmf-dist/tex/generic/hyphen/dumyhyph.tex)
(/usr/share/texmf-dist/tex/generic/hyphen/zerohyph.tex)
(/usr/share/texmf-dist/tex/generic/dehyph-exptl/dehypht-x-2021-02-26.tex
dehyph-exptl: using an 8-bit TeX engine.
(/usr/share/texmf-dist/tex/generic/dehyph-exptl/dehypht-x-2021-02-26.pat
German Hyphenation Patterns (Traditional Orthography) `dehypht-x' 2021-02-26 (W
L))) (/usr/share/texmf-dist/tex/generic/dehyph-exptl/dehyphn-x-2021-02-26.tex
dehyph-exptl: using an 8-bit TeX engine.
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(WL))) (/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-af.tex
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Coptic hyphenation patterns
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(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-fi.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-fi-x-school.tex
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(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-fi-x-school.tex)
) (/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-fr.tex
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(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-fr.tex))
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(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-fur.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-gl.tex
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(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-gl.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-ka.tex
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(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-t8m.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-ka.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-de-1901.tex
EC German hyphenation patterns (traditional orthography)
! I can't find file `dehypht.tex'.
l.29 \input dehypht.tex
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l.29 \input dehypht.tex
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This is pdfTeX, Version 3.141592653-2.6-1.40.22 (TeX Live 2021/Mageia) (preloaded format=latex)
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is a convex function, are represented by constraint
objects. Equality constraints are created by expressions of the form
Here f1
and f2
can be any objects for which the difference
f1 - f2
yields an affine function. Inequality constraints are
created by expressions of the form
where f1
and f2
can be any objects for which the difference
f1 - f2
yields a convex piecewise-linear function. The comparison
operators first convert the expressions to f1 - f2 == 0
, resp.,
f1 - f2 <= 0
, and then return a new constraint
object with
constraint function f1 - f2
.
In the following example we create three constraints
System Message: WARNING/2 (\newcommand{\ones}{{\bf 1}}
0 \preceq x \preceq \ones, \qquad \ones^T x = 2, )
latex exited with error
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German Hyphenation Patterns (Traditional Orthography) `dehypht-x' 2021-02-26 (W
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EC Afrikaans hyphenation patterns
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Hyphenation patterns for Ancient Greek))
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(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
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(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-hr.tex
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(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-eo.tex
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EC Estonian hyphenation patterns
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(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-et.tex))
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(/usr/share/texmf-dist/tex/generic/hyphen/zerohyph.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-fi.tex
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(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-fi.tex))
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(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-fi-x-school.tex)
) (/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-fr.tex
EC French hyphenation patterns
(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
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(/usr/share/texmf-dist/tex/generic/hyph-utf8/conversions/conv-utf8-ec.tex)
(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-fur.tex))
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(/usr/share/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-ka.tex))
(/usr/share/texmf-dist/tex/generic/hyph-utf8/loadhyph/loadhyph-de-1901.tex
EC German hyphenation patterns (traditional orthography)
! I can't find file `dehypht.tex'.
l.29 \input dehypht.tex
(Press Enter to retry, or Control-D to exit)
Please type another input file name:
! Emergency stop.
l.29 \input dehypht.tex
No pages of output.
Transcript written on latex.log.
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This is pdfTeX, Version 3.141592653-2.6-1.40.22 (TeX Live 2021/Mageia) (preloaded format=latex)
restricted \write18 enabled.
I can't find the format file `latex.fmt'!
for a variable of length 5.
>>> x = variable ( 5 , 'x' )
>>> c1 = ( x <= 1 )
>>> c2 = ( x >= 0 )
>>> c3 = ( sum ( x ) == 2 )
The built-in function len
returns the dimension of the
constraint function.
Constraints have four public attributes.
constraint. type
Returns '='
if the constraint is an equality constraint, and
‘<’ if the constraint is an inequality constraint.
constraint. value
Returns the value of the constraint function.
constraint. multiplier
For a constraint c
, c.multiplier
is a variable
object of dimension len(c)
. It is used to represent the
Lagrange multiplier or dual variable associated with the constraint.
Its value is initialized as None
, and can be modified by making
an assignment to c.multiplier.value
.
constraint. name
The name of the constraint. Changing the name of a constraint also
changes the name of the multiplier of c
. For example, the command
c.name = 'newname'
also changes
c.multiplier.name
to 'newname_mul'
.
Optimization Problems
Optimization problems are be constructed by calling the following
function.
cvxopt.modeling. op ( [ objective [ , constraints [ , name ] ] ] )
The first argument specifies the objective function to be minimized.
It can be an affine or convex piecewise-linear function with length 1,
a variable
with length 1, or a scalar constant (integer, float,
or 1 by 1 dense 'd'
matrix). The default value is 0.0.
The second argument is a single constraint
, or a list of
constraint
objects. The default value is an empty list.
The third argument is a string with a name for the problem.
The default value is the empty string.
The following attributes and methods are useful for examining
and modifying optimization problems.
op. objective
The objective or cost function. One can write to this attribute to
change the objective of an existing problem.
op. variables ( )
Returns a list of the variables of the problem.
op. constraints ( )
Returns a list of the constraints.
op. inequalities ( )
Returns a list of the inequality constraints.
op. equalities ( )
Returns a list of the equality constraints.
op. delconstraint ( c )
Deletes constraint c
from the problem.
op. addconstraint ( c )
Adds constraint c
to the problem.
An optimization problem with convex piecewise-linear objective and
constraints can be solved by calling the method solve
.
op. solve ( [ format [ , solver ] ] )
This function converts the optimization problem to a linear program in
matrix form and then solves it using the solver described in
the section Linear Programming .
The first argument is either 'dense'
or 'sparse'
, and
denotes the matrix types used in the matrix representation of the LP.
The default value is 'dense'
.
The second argument is either None
, 'glpk'
, or
'mosek'
, and selects one of three available LP solvers: the
default solver written in Python, the GLPK solver (if installed) or the
MOSEK LP solver (if installed); see the section Linear Programming . The
default value is None
.
The solver reports the outcome of optimization by setting the attribute
self.status
and by modifying the value
attributes of
the variables and the constraint multipliers of the problem.
If the problem is solved to optimality, self.status
is set to
'optimal'
. The value
attributes of the variables in
the problem are set to their computed solutions, and the
value
attributes of the multipliers of the constraints of the
problem are set to the computed dual optimal solution.
If it is determined that the problem is infeasible,
self.status
is set to 'primal infeasible'
.
The value
attributes of the variables are set to
None
. The value
attributes of the multipliers of
the constraints of the problem are set to a certificate of primal
infeasibility. With the 'glpk'
option, solve
does
not provide certificates of infeasibility.
If it is determined that the problem is dual infeasible,
self.status
is set to 'dual infeasible'
.
The value
attributes of the multipliers of the constraints of
the problem are set to None
. The value
attributes
of the variables are set to a certificate of dual infeasibility.
With the 'glpk'
option, solve
does not provide
certificates of infeasibility.
If the problem was not solved successfully, self.status
is set
to 'unknown'
. The value
attributes of the variables
and the constraint multipliers are set to None
.
We refer to the section Linear Programming for details on the algorithms and
the different solver options.
As an example we solve the LP
System Message: WARNING/2 (\begin{array}{ll}
\mbox{minimize} & -4x - 5y \\
\mbox{subject to} & 2x +y \leq 3 \\
& x +2y \leq 3 \\
& x \geq 0, \quad y \geq 0.
\end{array}
)
latex exited with error
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>>> from cvxopt.modeling import op
>>> x = variable ()
>>> y = variable ()
>>> c1 = ( 2 * x + y <= 3 )
>>> c2 = ( x + 2 * y <= 3 )
>>> c3 = ( x >= 0 )
>>> c4 = ( y >= 0 )
>>> lp1 = op ( - 4 * x - 5 * y , [ c1 , c2 , c3 , c4 ])
>>> lp1 . solve ()
>>> lp1 . status
'optimal'
>>> print ( lp1 . objective . value ())
[-9.00e+00]
>>> print ( x . value )
[ 1.00e+00]
>>> print ( y . value )
[ 1.00e+00]
>>> print ( c1 . multiplier . value )
[ 1.00e+00]
>>> print ( c2 . multiplier . value )
[ 2.00e+00]
>>> print ( c3 . multiplier . value )
[ 2.87e-08]
>>> print ( c4 . multiplier . value )
[ 2.80e-08]
We can solve the same LP in matrix form as follows.
>>> from cvxopt.modeling import op , dot
>>> x = variable ( 2 )
>>> A = matrix ([[ 2. , 1. , - 1. , 0. ], [ 1. , 2. , 0. , - 1. ]])
>>> b = matrix ([ 3. , 3. , 0. , 0. ])
>>> c = matrix ([ - 4. , - 5. ])
>>> ineq = ( A * x <= b )
>>> lp2 = op ( dot ( c , x ), ineq )
>>> lp2 . solve ()
>>> print ( lp2 . objective . value ())
[-9.00e+00]
>>> print ( x . value )
[ 1.00e+00]
[ 1.00e+00]
>>> print ( ineq . multiplier . value )
[1.00e+00]
[2.00e+00]
[2.87e-08]
[2.80e-08]
The op
class also includes two methods for writing and reading
files in
MPS format .
tofile(filename) :noindex:
If the problem is an LP, writes it to the file filename using the
MPS format. Row and column labels are assigned based on the variable
and constraint names in the LP.
fromfile(filename) :noindex:
Reads the LP from the file filename . The file must be a fixed-format
MPS file. Some features of the MPS format are not supported: comments
beginning with dollar signs, the row types ‘DE’, ‘DL’, ‘DG’, and ‘DN’,
and the capability of reading multiple righthand side, bound or range
vectors.