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2 LP Problem
The general formulation in TOMLAB for a linear programming problem is:
|
|
|
f(x) = cT x |
| |
|
| s/t |
| xL |
≤ |
x |
≤ |
xU |
| bL |
≤ |
A x |
≤ |
bU |
|
|
(1) |
where
c,
x,
xL,
xU 
Rn,
A Rm1 × n, and
bL,
bU Rm1. Equality constraints are defined by setting the lower bound to the upper bound.
Example problem:
|
|
|
f(x1,x2) = −7x1−5x2 |
| |
|
| s/t |
| x1+2x2 |
≤ |
6 |
| 4x1+x2 |
≤ |
12 |
| x1,x2 |
≥ |
0 |
|
|
(2) |
The following file defines this problem in TOMLAB.
File: tomlab/quickguide/lpQG.m
Open the file for viewing, and execute lpQG in Matlab.
% lpQG is a small example problem for defining and solving
% linear programming problems using the TOMLAB format.
Name = 'lpQG'; % Problem name, not required.
c = [-7 -5]'; % Coefficients in linear objective function
A = [ 1 2
4 1 ]; % Matrix defining linear constraints
b_U = [ 6 12 ]'; % Upper bounds on the linear inequalities
x_L = [ 0 0 ]'; % Lower bounds on x
% x_min and x_max are only needed if doing plots
x_min = [ 0 0 ]';
x_max = [10 10 ]';
% b_L, x_U and x_0 have default values and need not be defined.
% It is possible to call lpAssign with empty [] arguments instead
b_L = [-inf -inf]';
x_U = [];
x_0 = [];
% Assign routine for defining an LP problem. This allows the user
% to try any solver, including general nonlinear solvers.
Prob = lpAssign(c, A, b_L, b_U, x_L, x_U, x_0, Name,...
[], [], [], x_min, x_max, [], []);
% Calling driver routine tomRun to run the solver.
% The 1 sets the print level after optimization.
% Result.x_k contains the optimal decision variables.
% Result.f_k is the optimal value.
Result = tomRun('pdco', Prob, 1);
%Result = tomRun('lpSimplex', Prob, 1);
%Result = tomRun('minos', Prob, 1);
%Result = tomRun('snopt', Prob, 1);
%Result = tomRun('conopt', Prob, 1);
%Result = tomRun('knitro', Prob, 1);
%Result = tomRun('cplex', Prob, 1);
%Result = tomRun('xpress-mp', Prob, 1);
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