Models Mixed-Integer Quadratic Programming Problems: mipq prob

This page is part of TOMLAB Models. See TOMLAB Models.

In mipq_prob there are 4 mixed-integer quadratic programming test problems with sizes to about 120 variables and slightly more than 100 constraints. In order to define the problem n and solve it execute the following in Matlab:

Prob = probInit('miqp_prob',n); 
Result  = tomRun('',Prob);

The basic structure of a general mixed-integer quadratic programming problem is:

${\begin{array}{ll}\min \limits _{x}&f(x)={\frac {1}{2}}x^{T}Fx+c^{T}x\\&\\s/t&{\begin{array}{lcccl}x_{L}&\leq &x&\leq &x_{U},\\b_{L}&\leq &Ax&\leq &b_{U},~x_{j}\in \mathbb {N} \ ~~\forall j\in \$I\$\\\end{array}}\end{array}}$

where $c,x,x_{L},x_{U}\in \mathbb {R} ^{n}$, $A\in \mathbb {R} ^{m_{1}\times n}$, and $b_{L},b_{U}\in \mathbb {R} ^{m_{1}}$. The variables $x\in I$, the index subset of $1,...,n$ are restricted to be integers.

An example of a problem of this class, (that is also found in the TOMLAB quickguide) is mipqQG:

File: tomlab/quickguide/miqpQG.m

% miqpQG is a small example problem for defining and solving
% mixed-integer quadratic programming problems using the TOMLAB format.

c    = [-6 0]';
Name = 'XP Ref Manual MIQP';
F    = [4 -2;-2 4];
A    = [1 1];
b_L  = -Inf;
b_U  = 1.9;
x_L  = [0 0]';
x_U  = [Inf Inf]';

% Defining first variable as an integer
IntVars   = 1;

% Assign routine for defining a MIQP problem.
Prob = miqpAssign(F, c, A, b_L, b_U, x_L, x_U, [], ...
           IntVars, [], [], [], Name, [], []);

% Calling driver routine tomRun to run the solver.
% The 1 sets the print level after optimization.

Result = tomRun('cplex', Prob, 1);
%Result = tomRun('oqnlp', Prob, 1);
%Result = tomRun('miqpBB', Prob, 1);
%Result = tomRun('xpress-mp', Prob, 1);
%Result = tomRun('minlpBB', Prob, 1);