Question

I want to solve this linear programming (simplex) problem using MATLAB 7, but it returns

Exiting: the problem is unbounded.

This function

f = 2(15 s0 + 8s1 + 2576s2 + 744s3 + 427s4 + 8s5)

Should be minimized in such a way that two constraints for each observation are
satisfied

0.1s0 + 0.1s1 + 14.5s2 + 4s3 + 2.4s4 – a0 − a1 − 145a2 − 40a3 − 24a4 ≥ −2.2

0.1s0 + 0.1s1 + 14.5s2 + 4s3 + 2.4s4 + a0 + a1 + 145a2 + 40a3 + 24a4 ≥ 2.2

S5 and a5 are 0. I used

f = [15   8  2576  744  427 8   15   8  2576 744  427 8];

b = [-2.2; 2.2];

a = [0.1  0.1 14.5  0.4  2.4 0 -1 -1  -145 -40 -24 0 ; 0.1  0.1 14.5  4  2.4 0 1  1   145  40  24 0]; 

[x, fval, exitflag, output, lambda] = linprog(f, a, b)

What is the right way to solve this problem?

Answer 1

You didn’t constrain your s5 and a5 to actually be zero, since you set the corresponding coefficients in the a matrix to zero. Thus, they can take on any value, and the LP is unbounded.

To fix, add an equality constraint:

beq = [0; 0];
aeq = [0 0 0 0 0 1 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 1];
[x,fval,exitflag,output,lambda] = linprog(f,a,b,aeq,beq)

Or, just drop s5 and a5 from the LP since they don’t contribute at all.