Quickguide MIQP Problem: Difference between revisions
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Revision as of 03:44, 10 August 2011
This page is part of the Quickguide Manual. See Quickguide. |
The general formulation in TOMLAB for a mixed-integer quadratic programming problem is:
Failed to parse (unknown function "\MATHSET"): {\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 , the index subset of are restricted to be
integers. Equality constraints are defined by setting the lower
bound equal to the upper bound, i.e. for constraint : .
The following file illustrates how to solve a MIQP problem in TOMLAB.
File: tomlab/quickguide/miqpQG.m
Open the file for viewing, and execute miqpQG in Matlab.
% 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);