%% Linear Program Using the 'interior-point' Algorithm
% Solve a linear program using the 'interior-point' algorithm.
% For this example, use these linear inequality constraints:
%  x(1) + x(2) \le 2
% x(1) + x(2)/4 \le 1
% x(1) - x(2) \le 2
% -x(1)/4 - x(2) \le 1
% -x(1) - x(2) \le -1
% -x(1) + x(2) \le 2.

A = [1 1
    1 1/4
    1 -1
    -1/4 -1
    -1 -1
    -1 1];

b = [2 1 2 1 -1 2];

%
% Use the linear equality constraint x(1) + x(2)/4 = 1/2.

Aeq = [1 1/4];
beq = 1/2;

%
% Set these bounds:
% -1 \le x(1) \le 1.5
% -0.5 \le x(2) \le 1.25 .

lb = [-1,-0.5];
ub = [1.5,1.25];

%
% Use the objective function -x(1) - x(2)/3.

f = [-1 -1/3];

%
% Set options to use the 'interior-point' algorithm.

options = optimoptions('linprog','Algorithm','interior-point');

%
% Solve the linear program using the 'interior-point' algorithm.

x = linprog(f,A,b,Aeq,beq,lb,ub,options)

% Copyright 2012 The MathWorks, Inc.