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19 MINIMAXLIN Problem
The
linear minimax (
mimalin) problem is defined as
|
|
maxDx |
subject to |
xL |
≤ |
x |
≤ |
xU |
|
bL |
≤ |
Ax |
≤ |
bU |
|
(21) |
where
x,
xL,
xU Rn,
bL,
bU Rm1,
A
Rm1 × n and
D Rm2 × n.
The following file illustrates how to solve a linear minimax problem
in TOMLAB.
File: tomlab/quickguide/minimaxlinQG.m
Open the file for viewing, and execute minimaxlinQG in Matlab.
% minimaxlinQG is a small example problem for defining and solving
% linear minimax programming problems using the TOMLAB format.
Name = 'Linear Minimax Test 1';
x_0 = [1;1;1;1]; % Initial value
x_L = [-10;-10;-10;-10]; % Lower bounds on x
x_U = [10;10;10;10]; % Upper bounds on x
% Solve the problem min max Dx while eliminating abs for the final two
% residuals by adding them with reverse signs.
% i.e. min max [D_1; D_2; D_3; -D_2; -D_3];
D = [9 8 7 6; -4 5 -6 -2; 3 4 5 -6; 4 -5 6 2; -3 -4 -5 6]; % D Matrix
% Add the linear constraint -x(1) + x(2) + 2 >= 0
% Write the constraint as x(1) - x(2) <= 2
% The A matrix could be specified dense or sparse
% A = sparse([1 -1 0 0]);
A = [1 -1 0 0];
b_L = -inf;
b_U = 2;
c = zeros(4,1); % Dummy objective
% Generate an LP problem using the Tomlab Quick format
% Use mipAssign if solving a mixed-integer problem
Prob = lpAssign(c, A, b_L, b_U, x_L, x_U, x_0, Name);
Prob.QP.D = D;
Prob.f_Low = 0;
Prob.SolverInf = 'minos';
% One may set other solvers:
% Prob.SolverInf = 'cplex';
% Prob.SolverInf = 'xa';
% Prob.SolverInf = 'snopt';
% Prob.SolverInf = 'milpSolve';
% Set print level 1 to get output from PrintResult at the end
PriLev = 1;
Prob.PriLevOpt = 0;
Result = tomRun('infLinSolve', Prob, PriLev);
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