qld - Linear quadratic programming solver (original) (raw)

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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])

Arguments

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 (dimensionn). If there are no lower bound constraints, putci = []. If some components ofx 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 precision.

x

optimal solution found.

lagr

vector of Lagrange multipliers. If lower and upper-boundsci,cs are provided, lagr hasn + me + md components andlagr(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) constrainti 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

This function requires Q to be positive definite, if it is not the case, one may use the The contributed toolbox "quapro".

Examples

C1= [1,-1,1,0,3,1; -1,0,-3,-4,5,6; 2,5,3,0,1,0]; b1=[1;2;3];

C2=[0,1,0,1,2,-1; -1,0,2,1,1,0]; b2=[-1;2.5];

ci=[-1000;-10000;0;-1000;-1000;-1000];cs=[10000;100;1.5;100;100;1000];

p=[1;2;3;4;5;6]; Q=eye(6,6);

C=[C1;C2]; b=[b1;b2]; me=3; [x,lagr]=qld(Q,p,C,b,ci,cs,me)

See Also

• qpsolve — linear quadratic programming solver
• optim — non-linear optimization routine

The contributed toolbox "quapro" may also be of interest, in particular for singular Q.

Authors

K.Schittkowski

, University of Bayreuth, Germany

A.L. Tits and J.L. Zhou

, University of Maryland

Used Functions

ql0001.f inmodules/optimization/src/fortran/ql0001.f