How to use fminimax

Hello, I would like to use fminimax to solve the following problem. Could someone help me please?

My f(x,w,y,z) is quite complex, so lets say it is just f=x+w+y+z

My main question is how to use fminimax, because I have only one function, but using MIN with y,z and MAX with x,w. I have tried this code for my function:

function f = myfun(x)
  f(1) = x(1)+x(2)
  f(2) = x(3)+x(4)
end

[x,fval] = fminimax(@myfun,...)

However, it looks quite wrong. Even using just f = x(1)+x(2)+x(3)+x(4) it doen't seems right.

Mathworks documentation is poor for this command: https://www.mathworks.com/help/optim/ug/fminimax.html

PS.: I am trying to use robust optmization to solve a planning problem.

Thanks for any help!

Answer 1

[Bruno Luong]

I believe for FMINIMAX the inner-max (min for your case) is performed on discrete set of variables, which corresponds the length of output vector F of the user FUN.

In your case since you have continuous inner-min, so I guess FMINIMAX not directly applicable.