Except for some unfortunate terms, as @Erling pointed out, this would be a Geometric Program which CVX could handle. See Geometric programming mode — CVX Users' Guide and read A Tutorial on Geometric Programming for a more in depth understanding.
But his isn’t horseshoes, hand grenades, or nuclear weapons, so close doesn’t count.
The CVX Users’ Guide is the tutorial CVX Users’ Guide — CVX Users' Guide . The are CVX examples at Example library | CVX Research, Inc. as well as in this forum.