Scilab Function
Last update : 28/12/2008
qld - linear quadratic programming solver
Calling Sequence
- [x,lagr]=qld(Q,p,C,b,ci,cs,me [,tol])
- [x,lagr,info]=qld(Q,p,C,b,ci,cs,me [,tol])
Parameters
-
Q: real positive definite symmetric matrix (dimension n x n).
-
p: real (column) vector (dimension n)
-
C: real matrix (dimension (me + md) x n)
-
b: RHS column vector (dimension (me + md))
-
ci: column vector of lower-bounds (dimension n). If
there are no lower bound constraints, put ci = []. If
some components of x are bounded from below, set the
other (unconstrained) values of ci to a very large
negative number (e.g. ci(j) =
-number_properties('huge').
-
cs: column vector of upper-bounds. (Same remarks as above).
-
me: number of equality constraints (i.e. C(1:me,:)*x = b(1:me))
-
tol:Floatting point number, required précision.
-
x: optimal solution found.
-
lagr: vector of Lagrange multipliers. If lower and upper-bounds
ci,cs are provided, lagr has n +
me + md components and lagr(1:n) is the
Lagrange vector associated with the bound constraints and
lagr (n+1 : n + me + md) is the Lagrange vector
associated with the linear constraints. (If an upper-bound
(resp. lower-bound) constraint i is active
lagr(i) is > 0 (resp. <0). If no bounds are
provided, lagr has only me + md
components.
-
info: integer, return the execution status instead of sending
errors.
info==1 : Too many iterations needed
info==2 : Accuracy insufficient to statisfy convergence criterion
info==5 : Length of working array is too short
info==10: The constraints are inconsistent
Description
Minimize 0.5*x'*Q*x + p'*x
under the constraints
C(j,:) x = b(j), j=1,...,me
C(j,:) x <= b(j), j=me+1,...,me+md
ci <= x <= cs
This function requires Q to be positive definite, if it is
not the case, one may use the quapro function.
Examples
//Find x in R^6 such that:
//C1*x = b1 (3 equality constraints i.e me=3)
C1= [1,-1,1,0,3,1;
-1,0,-3,-4,5,6;
2,5,3,0,1,0];
b1=[1;2;3];
//C2*x <= b2 (2 inequality constraints)
C2=[0,1,0,1,2,-1;
-1,0,2,1,1,0];
b2=[-1;2.5];
//with x between ci and cs:
ci=[-1000;-10000;0;-1000;-1000;-1000];cs=[10000;100;1.5;100;100;1000];
//and minimize 0.5*x'*Q*x + p'*x with
p=[1;2;3;4;5;6]; Q=eye(6,6);
//No initial point is given;
C=[C1;C2] ; //
b=[b1;b2] ; //
me=3;
[x,lagr]=qld(Q,p,C,b,ci,cs,me)
//Only linear constraints (1 to 4) are active (lagr(1:6)=0):
See Also
quapro, optim,
Authors
-
K.Schittkowski, University of Bayreuth, Germany
-
A.L. Tits and J.L. Zhou , University of Maryland
Used Function
ql0001.f in routines/optim directory