Solves a linear quadratic problem.
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( ... )
a n x n matrix of doubles, where n is number of variables, represents coefficients of quadratic in the quadratic problem.
a n x 1 matrix of doubles, where n is number of variables, represents coefficients of linear in the quadratic problem
a m x n matrix of doubles, represents the linear coefficients in the inequality constraints
a column vector of doubles, represents the linear coefficients in the inequality constraints
a meq x n matrix of doubles, represents the linear coefficients in the equality constraints
a vector of doubles, represents the linear coefficients in the equality constraints
a n x 1 matrix of doubles, where n is number of variables, contains lower bounds of the variables.
a n x 1 matrix of doubles, where n is number of variables, contains upper bounds of the variables.
a m x 1 matrix of doubles, where m is number of constraints, contains initial guess of variables.
a list containing the the parameters to be set.
a nx1 matrix of doubles, the computed solution of the optimization problem.
a 1x1 matrix of doubles, the function value at x.
Integer identifying the reason the algorithm terminated.
Structure containing information about the optimization.
Structure containing the Lagrange multipliers at the solution x (separated by constraint type).
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.
+//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; |  |  |
//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) | | |