Linear quadratic programming solver builtin (original) (raw)

Scilab 5.3.3

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Scilab help >> Optimization and Simulation > qp_solve

qp_solve

linear quadratic programming solver builtin

Calling Sequence

[x [,iact [,iter [,f]]]]=qp_solve(Q,p1,C1,b,me)

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). This matrix may be dense or sparse.

b

RHS column vector (dimension m=(me + md))

me

number of equality constraints (i.e. x'*C(:,1:me) = b(1:me)')

x

optimal solution found.

iact

vector, indicator of active constraints. The first non zero entries give the index of the active constraints

iter

2x1 vector, first component gives the number of "main" iterations, the second one says how many constraints were deleted after they became active.

Description

This function requires Q to be symmetric positive definite. If this hypothesis is not satisfied, one may use the contributedquapro toolbox.

Examples

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

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

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

me=3; [x,iact,iter,f]=qp_solve(Q,p,[C1 C2],[b1;b2],me)

See Also

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

Memory requirements

Let r be

Then the memory required by qp_solve during the computations is

Authors

S. Steer

INRIA (Scilab interface)

Berwin A. Turlach

School of Mathematics and Statistics (M019), The University of Western Australia, Crawley, AUSTRALIA (solver code)

References

Used Functions

qpgen2.f and >qpgen1.f (also named QP.solve.f) developped by Berwin A. Turlach according to the Goldfarb/Idnani algorithm