CVX formulation is incorrect. What is inside the max min should be concave and it is concave (I proved it). The problem is that what is inside max min looks like that (concave)^2 which violates the DCP ruleset as the composition is not always concave (although it is concave in this case)

I tried to use pow_abs(-concave,2) but then what is inside max min is convex and it cannot be solved.

Thank you for your response. That was quicker that I thought it would be. I believe I am pretty sure the problem is convex. As a start the constraints are linear as you see in the problem definition and here is how I proved that the objective function is concave:

I read the FAQ and I am not sure if you can help me reformulate the objective function to be seen concave inside the max-min as it is mathematically.

Thank you very much. I really appreciate your help.

Please read the section of the FAQ entitled, “But I can’t use the DCP rules alone to prove it; I had to use other principles, like a derivative test or a secant test, as well.”