# Formulating the max min problem in CVX with concave square dinside

Hi

I have trouble formulating my Max Min problem in CVX.

My MATLAB code is as follows

cvx_begin

variable x(M,K)

maximize(min((sum(x.^0.5.*C)).^2./(1+sum(B))))

subject to

for m =1:M

x(m,:)*transpose(A(m,:)) ==1
x(m,: ) >= zeros(1,K)

end

cvx_end

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.

I do not know how to solve it.

Thank you.

I know you say you proved convexity here: but exactly how did you do so? The how matters, and is covered in the FAQ above.

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.”

Thank you.

It seems that it cannot be formulated to CVX.

That was certainly my guess, sorry CVX won’t work for you!

I have nearly the same question as you, so how do you solve this problem finally?Could you please give me some idea?

Your problem is different, and not convex. CVX cannot solve it.