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5 MIQP Problem
The general formulation in TOMLAB for a mixed-integer quadratic
programming problem is:
|
|
|
|
|
s/t |
xL |
≤ |
x |
≤ |
xU, |
bL |
≤ |
A x |
≤ |
bU,
xj N j I |
|
|
(6) |
where
c,
x,
xL,
xU Rn,
A Rm1
× n, and
bL,
bU Rm1. The variables
x
I, the index subset of 1,...,
n are restricted to be
integers. Equality constraints are defined by setting the lower
bound equal to the upper bound, i.e. for constraint
i:
bL(
i)
=
bU(
i).
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);
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