x2linprog.m

来自「实用化工计算机模拟：MATLAB在化学工程中的应用 附录光盘程序」· M 代码 · 共 47 行

% x2LinProg.m
% 线性规划--函数linprog()的简单应用示例
%
%   Author: HUANG Huajiang
%   Copyright 2003 UNILAB Research Center, 
%   East China University of Science and Technology, Shanghai, PRC
%   $Revision: 1.0 $  $Date: 2002/05/31 $
%
% 优化问题Optimization problem：
% min -2x1 - x2 + x3
% s.t. x1 + x2 + 2x3 = 6 
%      x1 + 4x2 - x3 <= 4
%      x1>=0,x2>=0,x3<=5
%
% 注意：原问题不是标准形式，要先把原问题转化为最小化标准形式
% Notes: The original problem should be firstly transformed into the 
%   standard form of minimization as followings:
%   Min f'(x)   
%   s.t. AX <= b
%        AeqX = beq
%        LB <= X <= UB
%   that is：
%   min  -2x1 - x2 - x3'  % 技巧：以（-x3'）代替x3   substitute （-x3'）for x3
%   s.t. 
%        x1 + 4x2 + x3' <= 4
%        x1 + x2 - 2x3' = 6
%        x1>=0,x2>=0,x3'>=-5

clear
clc
f = [-2 -1 -1]';     
A = [1  4   1
     0  0   0
     0  0   0 ];
b = [4 0 0]';
Aeq = [1 1 -2];
beq = [6];
lb = [0 0 -5];

[x, fval] = linprog(f,A,b,Aeq,beq,lb)
x(3) = -x(3);
disp('The optimal sulution:')
disp(x)
disp('The objective value of the original function:')
disp(fval)