Problem While Doing Libprog (Problem is unbounded)

Hey guys, I was trying to write a code to solve for a problem of 9 variables but with 4 constraints. Here's the code:

A=[1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

0.1 0.1 0.4 0.6 0.3 0.3 0.3 0.5 0.2

0.1 0.3 0.5 0.3 0.3 0.4 0.2 0.4 0.3

0.8 0.6 0.1 0.1 0.4 0.3 0.5 0.1 0.5];

B=[1 0.3 0.3 0.4];

Z=[4.1 4.3 5.8 6.0 7.6 7.5 7.3 6.9 7.3];

[x,fval] = linprog(Z,A,B);

I need to get the final value of the problem which the problem needs to be minimize.

[Torsten]

The problem is unbounded.

Maybe you forgot to set x(i) >= 0 (i=1,...,9) as a constraint in "lb" ?

Answer 1

[Sam Chak]

Hi @Loke Yan Kuang

You can also check if a feasible solution exists in other solver such as fmincon.

A = [1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0    
   0.1 0.1 0.4 0.6 0.3 0.3 0.3 0.5 0.2
   0.1 0.3 0.5 0.3 0.3 0.4 0.2 0.4 0.3
   0.8 0.6 0.1 0.1 0.4 0.3 0.5 0.1 0.5]

b = [1 0.3 0.3 0.4]

f = [4.1 4.3 5.8 6.0 7.6 7.5 7.3 6.9 7.3]

lb = zeros(length(f), 1);
ub = [];

x0 = repmat(100, length(f), 1);

[x, fval, exitflag] = fmincon(@(x) dot(f, x), x0, A, b, [], [], lb, ub)

x =

1.0e-06 *

0.4958

0.4733

0.3499

0.3378

0.2659

0.2696

0.2768

0.2935

0.2768

fval =

1.8233e-05

exitflag =

1

For more info, please look up the following:

https://www.mathworks.com/help/optim/ug/fmincon.html?searchHighlight=fmincon&s_tid=srchtitle_fmincon_1#busog7r-exitflag

Answer 2

[Loke Yan Kuang]

Hi, I have found the mistakes in the code. This would be the new one and I will put in the result as well

A=[1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

0.1 0.1 0.4 0.6 0.3 0.3 0.3 0.5 0.2

0.1 0.3 0.5 0.3 0.3 0.4 0.2 0.4 0.3

0.8 0.6 0.1 0.1 0.4 0.3 0.5 0.1 0.5];

B=[1 0.3 0.3 0.4];

Z=[4.1 4.3 5.8 6.0 7.6 7.5 7.3 6.9 7.3];

[X,New_Cost]=linprog(Z,[],[],A,B,zeros(size(Z)),[],[]) %

The result:

Optimal solution found.

X =

0

0.6000

0

0.4000

0

0

0

0

0

New_Cost =

4.9800

[Torsten]

You put A, b at the wrong position in the call to "linprog".