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6 MIQQ Problem
The general formulation in TOMLAB for a mixed-integer quadratic
programming problem with quadratic constraints is:
|
|
|
s/t |
xL |
≤ |
x |
≤ |
xU |
|
bL |
≤ |
Ax |
≤ |
bU |
|
|
|
xT Q(i) x + a(i)T x |
≤ |
rU(i), |
i=1,…,nqc |
|
|
|
xi integer |
|
i I |
|
(7) |
where
c,
x,
xL,
xU,
a(i) Rn,
F,
Q(i) Rn× n,
A Rm×
n and
bL,
bU Rm.
rU(i) is a
scalar. The variables
x I, the index subset of 1,...,
n,
are restricted to be integers.
The following file illustrates how to solve a MIQQ problem in
TOMLAB.
File: tomlab/quickguide/miqqQG.m
Open the file for viewing, and execute miqqQG in Matlab.
% miqqQG is a small example problem for defining and solving
% mixed-integer quadratic programming problems with quadratic constraints
% using the TOMLAB format.
Name = 'MIQQ Test Problem 1';
f_Low = -1E5;
x_opt = [];
f_opt = [];
IntVars = [0 0 1];
F = [2 0 0;0 2 0;0 0 2];
A = [1 2 -1;1 -1 1];
b_L = [4 -2]';
b_U = b_L;
c = zeros(3,1);
x_0 = [0 0 0]';
x_L = [-10 -10 -10]';
x_U = [10 10 10]';
x_min = [0 0 -1]';
x_max = [2 2 1]';
% Adding quadratic constraints
qc(1).Q = speye(3,3);
qc(1).a = zeros(3,1);
qc(1).r_U = 3;
qc(2).Q = speye(3,3);
qc(2).a = zeros(3,1);
qc(2).r_U = 5;
Prob = miqqAssign(F, c, A, b_L, b_U, x_L, x_U, x_0, qc,...
IntVars, [], [], [],...
Name, [], [],...
x_min, x_max, f_opt, x_opt);
Result = tomRun('cplex', Prob, 1);
% Result = tomRun('minlpBB', Prob, 1);
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