We know that
maximize sum(-x.logx) will violate the DCP ruleset .We can use
maximize sum(entr(x)) to solve this problem.
But how to convert this problem?
maximize ΣΣX(i,j)（-log（X(i)）where X[i] is the sum of i row of X

Ps: I am not a native speaker .I am sorry if I don’t express myself clearlyl.

Thank you first .but i still have questions . we know logx is concave,but xlogx is convex.And I have prove that my question is a convex problem.And I use function entr to have solce my problem .But sometimes it doesn’t work well .Thank you ,I can’t give you images to explain my problem.

Actually, I misread your problem, I apologize. It may indeed be convex, but I frankly have no idea how you would formulate it in CVX. It is not easy to use logarithms in CVX, since the solvers do not handle them. Perhaps another reader can help.

In the end ,this problem can be solved.I really thank you.I am a new learner of convex optimization,it’s really kind of you to help me.I am not a native speaker ,I hope I don’t misunderstand you.