Using Linprog to perform a MaxMin optimization.

Hi,

I am trying to solve a MaxMin , 2 player zero-sum game kind of problem using linprog function:

Our Professor, wanted us to use that to come up with the MaxMin solution:

I know how to solve LP using linprog, over single objective functions like this:

Non-matlab compatible form:

max: 2x+5y

s.t : x+y <= 1000

x+5y <= 2000

x>= 0; y >=0;

Change it to a form that linprog likes:

min: -2x-5y

s.t : x+y <= 1000

x+5y <= 2000

x>= 0; y >=0;

f = [-2,-5]

A = [1 1; 1 5]

b = [1000 2000]

xright = linprog(f,A,b)

However, for a MaxMin problem, the objective looks like this:

v = min(-3z1+2z2, z1-z2)

min -v

subject to:

some constraints.

How do I represent V in matlab. There are 2 things under consideration separated by a comma min(-3z1+2z2, z1-z2).

For a normal LP problem, I can do it, without any issues , as there is only onle objective being dealt with.

Thanks

[Sulaymon Eshkabilov]

Have you seen this extensive help documentation of MATLAB with a few nice examples: https://www.mathworks.com/help/optim/ug/linprog.html

[Whitchurch Muthumani]

Yes I did.

I did eventually use linprog, but with the

Problem object. In this object I specified my constraints.

I had to set the optimization objection to V, instead of min(-3z1+2z2, z1-z2), and do linprog on it, with additional constraints over V. As mentioned in the answer which I accepted.

Answer 1

[Torsten]

min: -v
v <= -3*z1 + 2*z2
v <= z1 - z2
+ additional constraints

[Whitchurch Muthumani]

Thank you.

This is the very same approach I came up with.

As you stated, I set the objective to -v and

used the constraints with it.

Additionaly, I learnt about the cvx solver, and used that one.

It gave me the benefit of not having to change the signs, as is the case with linprog.

Both approaches gave the same answer.

Thank you for your help.