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])

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 (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 precision. : :x optimal solution found. : :lagr vector of Lagrange multipliers. If lower and upper-bounds `ci,

cs` are provided, lagr has me + md + 2* n components. The components lagr(1:me + md) are associated with the linear constraints and lagr (me + md + 1 : 2 * n) are associated with the lower and upper bounds 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. On successful termination, all values of lagr with respect to inequalities and bounds should be greater or equal to zero.

: :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 contributed toolbox ” quapro”.

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

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

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

Used Functions

ql0001.f in modules/optimization/src/fortran/ql0001.f