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:

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{array}{ll}\min\limits_{x} & f(x) = \frac{1}{2} x^T F x + c^T x \\ & \\s/t & \begin{array}{lcccl}x_{L} & \leq & x & \leq & x_{U}, \\b_{L} & \leq & A x & \leq & b_{U}, ~x_{j} \in \MATHSET{N}\ ~~\forall j \in $I$ \\\end{array}\end{array} }

where Failed to parse (unknown function "\MATHSET"): {\displaystyle c, x, x_L, x_U \in \MATHSET{R}^n} , Failed to parse (unknown function "\MATHSET"): {\displaystyle A \in \MATHSET{R}^{m_1 \times n}} , and Failed to parse (unknown function "\MATHSET"): {\displaystyle b_L,b_U \in \MATHSET{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);