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qpipopt

Solves a linear quadratic problem.

Calling Sequence

xopt = qpipopt(nbVar,nbCon,Q,p,LB,UB,conMatrix,conLB,conUB)
[xopt,fopt,exitflag,output,lamda] = qpipopt( ... )

Parameters

nbVar :

a 1 x 1 matrix of doubles, number of variables

nbCon :

a 1 x 1 matrix of doubles, number of constraints

Q :

a n x n matrix of doubles, where n is number of variables, represents coefficients of quadratic in the quadratic problem.

p :

a 1 x n matrix of doubles, where n is number of variables, represents coefficients of linear in the quadratic problem

LB :

a 1 x n matrix of doubles, where n is number of variables, contains lower bounds of the variables.

UB :

a 1 x n matrix of doubles, where n is number of variables, contains upper bounds of the variables.

conMatrix :

a m x n matrix of doubles, where n is number of variables and m is number of constraints, contains matrix representing the constraint matrix

conLB :

a m x 1 matrix of doubles, where m is number of constraints, contains lower bounds of the constraints.

conUB :

a m x 1 matrix of doubles, where m is number of constraints, contains upper bounds of the constraints.

xopt :

a 1xn matrix of doubles, the computed solution of the optimization problem.

fopt :

a 1x1 matrix of doubles, the function value at x.

exitflag :

Integer identifying the reason the algorithm terminated.

output :

Structure containing information about the optimization.

lambda :

Structure containing the Lagrange multipliers at the solution x (separated by constraint type).

Description

Search the minimum of a constrained linear quadratic optimization problem specified by : find the minimum of f(x) such that

We are calling IPOpt for solving the quadratic problem, IPOpt is a library written in C++. The code has been written by ​Andreas Wächter and ​Carl Laird.

Examples

//Find x in R^6 such that:

conMatrix= [1,-1,1,0,3,1;
-1,0,-3,-4,5,6;
2,5,3,0,1,0
0,1,0,1,2,-1;
-1,0,2,1,1,0];
conLB=[1 2 3 -%inf -%inf]';
conUB = [1 2 3 -1 2.5]';
//with  x between ci and cs:
lb=[-1000 -10000 0 -1000 -1000 -1000];
ub=[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);
nbVar = 6;
nbCon = 5;
[xopt,fopt,exitflag,output,lambda]=qpipopt(nbVar,nbCon,Q,p,lb,ub,conMatrix,conLB,conUB)

Examples

//min. -8*x1 -16*x2 + x1^2 + 4* x2^2
//  such that
//     x1 + x2 <= 5,
//     x1 <= 3,
//     x1 >= 0,
//     x2 >= 0
conMatrix= [1 1];
conLB=[-%inf];
conUB = [5];
//with  x between ci and cs:
lb=[0,0];
ub=[3,%inf];
//and minimize 0.5*x'*Q*x + p'*x with
p=[-8,-16];
Q=[1,0;0,4];
nbVar = 2;
nbCon = 1;
[xopt,fopt,exitflag,output,lambda] = qpipopt(nbVar,nbCon,Q,p,lb,ub,conMatrix,conLB,conUB)

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