qpipoptmat

Parameters

H : -: a symmetric matrix of double, represents coefficients of quadratic in the quadratic problem.
f : -: a vector of double, represents coefficients of linear in the quadratic problem
A : -: a matrix of double, represents the linear coefficients in the inequality constraints A⋅x ≤ b.
b : -: a vector of double, represents the linear coefficients in the inequality constraints A⋅x ≤ b.
Aeq : -: a matrix of double, represents the linear coefficients in the equality constraints Aeq⋅x = beq.
beq : -: a vector of double, represents the linear coefficients in the equality constraints Aeq⋅x = beq.
lb : -: a vector of double, contains lower bounds of the variables.
ub : -: a vector of double, contains upper bounds of the variables.
x0 : -: a vector of double, contains initial guess of variables.
param : -: a list containing the parameters to be set.
xopt : -: a vector of double, the computed solution of the optimization problem.
fopt : -: a double, the value of the function at x.
exitflag : -: The exit status. See below for details.
output : -: The structure consist of statistics about the optimization. See below for details.
lambda : -: The structure consist of the Lagrange multipliers at the solution of problem. See below for details.

Description

Search the minimum of a constrained linear quadratic optimization problem specified by :

The routine calls Ipopt for solving the quadratic problem, Ipopt is a library written in C++.

The options allows the user to set various parameters of the Optimization problem. -It should be defined as type "list" and contains the following fields. -

Syntax : options= list("MaxIter", [---], "CpuTime", [---]);
MaxIter : a Scalar, containing the Maximum Number of Iteration that the solver should take.
CpuTime : a Scalar, containing the Maximum amount of CPU Time that the solver should take.
Default Values : options = list("MaxIter", [3000], "CpuTime", [600]);

The exitflag allows to know the status of the optimization which is given back by Ipopt. -

exitflag=0 : Optimal Solution Found
exitflag=1 : Maximum Number of Iterations Exceeded. Output may not be optimal.
exitflag=2 : Maximum CPU Time exceeded. Output may not be optimal.
exitflag=3 : Stop at Tiny Step.
exitflag=4 : Solved To Acceptable Level.
exitflag=5 : Converged to a point of local infeasibility.

For more details on exitflag see the ipopt documentation, go to http://www.coin-or.org/Ipopt/documentation/

The output data structure contains detailed informations about the optimization process. -It has type "struct" and contains the following fields. -

output.iterations: The number of iterations performed during the search
output.constrviolation: The max-norm of the constraint violation.

The lambda data structure contains the Lagrange multipliers at the end -of optimization. In the current version the values are returned only when the the solution is optimal. -It has type "struct" and contains the following fields. -

lambda.lower: The Lagrange multipliers for the lower bound constraints.
lambda.upper: The Lagrange multipliers for the upper bound constraints.
lambda.eqlin: The Lagrange multipliers for the linear equality constraints.
lambda.ineqlin: The Lagrange multipliers for the linear inequality constraints.

Examples

//Ref : example 14 :
-//https://www.me.utexas.edu/~jensen/ORMM/supplements/methods/nlpmethod/S2_quadratic.pdf
-// min. -8*x1*x1 -16*x2*x2 + x1 + 4*x2
-// such that
-//    x1 + x2 <= 5,
-//    x1 <= 3,
-//    x1 >= 0,
-//    x2 >= 0
-H = [2 0
-0 8];
-f = [-8; -16];
-A = [1 1;1 0];
-b = [5;3];
-lb = [0; 0];
-ub = [%inf; %inf];
-[xopt,fopt,exitflag,output,lambda] = qpipoptmat(H,f,A,b,[],[],lb,ub)
-// Press ENTER to continue

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'*H*x + f'*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,x0,param)

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qpipoptmat

Calling Sequence

Parameters

Description

Examples

Examples

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