How to rewrite this constraint function subject to DCP rules?

Hi there,

I’m trying to solve the following optimization problem:

where and are both n-by-1 vectors, I wrote in matlab the following:


    variable X(2*n,1) nonnegative
    minimize [ones(1,n), zeros(1,n)] * X;
    subject to
        log(1 + c * pow_p([eye(n),zeros(n)]*X,-2)) + log(1+power(1/4,[zeros(n),eye(n)]*X)) <= d;
        [zeros(1,n),ones(1,n)] * X <= R;


I’ve managed to write and according to DCP rules using and respectively, but there’s still the problem of log{ (convex) } of the first term in the first constraint function. But is indeed convex.

So my question is how to rewrite the first constraint function that obeys the DCP rules?

Thank you.

Unfortunately, I doubt it is possible. CVX will likely not be able to solve this problem. I will take it at your word that this function is convex, nevertheless, CVX does not attempt to support every convex problem, as discussed in the FAQ.