How can I change the convergence condition in linprog?

I have very simple linear program as follows

min 150*x1+230*x2+260*x3
subject to
x1+x2+x3<=500
x1,x2,x3>=0

The optimal solution of the above problem is trivial and it is x=0. To solve this problem, I run the following code

f=[150;230;260];
A=[1 1 1];
b=500;
x=linprog(f,A,b,[],[],zeros(3,1));

and I obtain

x =
   1.0e-11 *

      0.9929
      0.7471
      0.6562

To obtain the exact solution (i.e., x=0), what can I do?

Thank you in advance,

Derya

Answer 1

[Alan Weiss]

There are different approaches depending on which MATLAB version you are running. The reason for the slight inaccuracy is that the default linprog algorithm is 'interior-point', which is fast and robust but can lead to slight inaccuracies in the reported solution.

So the solution for you is not to use an interior-point solver if you want the most accuracy (but you can lose robustness, memory efficiency, and solver time). For example,

options = optimoptions('linprog','Algorithm','active-set');
f=[150;230;260];
A=[1 1 1];
b=500;
x=linprog(f,A,b,[],[],zeros(3,1),[],[],options);

returns the following on my computer:

Optimization terminated.

x =

     0
     0
     0

Alan Weiss

MATLAB mathematical toolbox documentation

[DD]

Thank you Alan.

I am using MATLAB R2012a. The command you suggest ( options = optimoptions('linprog','Algorithm','active-set') ) gives the following error

Undefined function 'optimoptions' for input arguments of type 'char'.

Actually, I am using simplex algorithm by running the following command

options = optimset('Simplex','on');

Is there any way of obtaining x=0 while using simplex algorithm?

[Alan Weiss]

optimoptions was introduced in R2013a. For your MATLAB version, as documented the way to use the simplex algorithm is

 options = optimset('LargeScale', 'off', 'Simplex', 'on');
 x = linprog(f,A,b,[],[],zeros(3,1),[],[],options);

You could also try using the medium scale algorithm by simply setting

 options = optimset('LargeScale', 'off');

Alan Weiss

MATLAB mathematical toolbox documentation

[DD]

It seems that I was making mistake while using "options". You solved my problem :) Thank you Alan.