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qpipoptmat

Solves a linear quadratic problem.

Calling Sequence

x = qpipoptmat(H,f)
x = qpipoptmat(H,f,A,b)
x = qpipoptmat(H,f,A,b,Aeq,beq)
x = qpipoptmat(H,f,A,b,Aeq,beq,lb,ub)
x = qpipoptmat(H,f,A,b,Aeq,beq,lb,ub,x0)
x = qpipoptmat(H,f,A,b,Aeq,beq,lb,ub,x0,param)
[xopt,fopt,exitflag,output,lamda] = qpipoptmat( ... )

Parameters

H :

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

f :

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

A :

a vector of doubles, represents the linear coefficients in the inequality constraints

b :

a vector of doubles, represents the linear coefficients in the inequality constraints

Aeq :

a matrix of doubles, represents the linear coefficients in the equality constraints

beq :

a vector of doubles, represents the linear coefficients in the equality constraints

LB :

a vector of doubles, where n is number of variables, contains lower bounds of the variables.

UB :

a vector of doubles, where n is number of variables, contains upper bounds of the variables.

x0 :

a vector of doubles, contains initial guess of variables.

param :

a list containing the the parameters to be set.

xopt :

a vector of doubles, the computed solution of the optimization problem.

fopt :

a double, 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:

Aeq= [1,-1,1,0,3,1;
-1,0,-3,-4,5,6;
2,5,3,0,1,0];
beq=[1; 2; 3];
A= [0,1,0,1,2,-1;
-1,0,2,1,1,0];
b = [-1; 2.5];
lb=[-1000; -10000; 0; -1000; -1000; -1000];
ub=[10000; 100; 1.5; 100; 100; 1000];
x0 = repmat(0,6,1);
param = list("MaxIter", 300, "CpuTime", 100);
//and minimize 0.5*x'*Q*x + p'*x with
f=[1; 2; 3; 4; 5; 6]; H=eye(6,6);
[xopt,fopt,exitflag,output,lambda]=qpipoptmat(H,f,A,b,Aeq,beq,lb,ub,[],param)
clear H f A b Aeq beq lb ub;

Examples

//Find the value of x that minimize following function
// f(x) = 0.5*x1^2 + x2^2 - x1*x2 - 2*x1 - 6*x2
// Subject to:
// x1 + x2 ≤ 2
// –x1 + 2x2 ≤ 2
// 2x1 + x2 ≤ 3
// 0 ≤ x1, 0 ≤ x2.
H = [1 -1; -1 2];
f = [-2; -6];
A = [1 1; -1 2; 2 1];
b = [2; 2; 3];
lb = [0; 0];
ub = [%inf; %inf];
[xopt,fopt,exitflag,output,lambda] = qpipoptmat(H,f,A,b,[],[],lb,ub)

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