Part of my problem is maximizing the minimum magnitude squared of vector elements (x = [x_i]). This is not a convex problem as min is taking convex expressions.
One way to work with it is by maximizing g = log_prod(d(x)), where d=[d_i] and d_i = |x_i|^2. log_prod is concave and nonincreasing, and d is convex of x. Such composition is concave, so maximizing g is a convex problem. However, CVX is not accepting such formulation.
Why is it difficult for CVX to discover such concavity? does it help to build an atom for g?
