Hello, I am trying to solve this convex proble, I am stuck in the object function. How to rewrite it to the form which cvx accepts?

variables are Wu and Wd, other parameters are known, function y(W) is convex in a part of region, which is proved in the paper. In this problem, W is constrained within the convex region.

When I write term "wd*exp[]", there is an error saying Cannot perform the operation: {real affine} .* {convex}, wd is affine, exp[] is convex. How can I solve this?

I try to use exp(log(wd))*exp[], it becomes exp(log(wd)+[]), there is still an error saying can’t perform the operation concave+convex. exp(log(wd)) is concave.

HELP ME PLEASE!

If a function is only convex in a portion of its “natural” domain, even if there are constraints constraining to that portion, it is usually the case that no one can find a way if representing it in CVX.

Nevertheless, perhaps a conic refromulation guru will come along and come up with a reformulation. But don’t count on it.

Thank you Mark! Anyway I know I might need to seek other methods. But I still want to check with you Mark, this figure is a demonstration of y(W), it is convex in (0,W0), the constraints of W is W belongs to (0, Wth), in this case, it is not possible to solve using cvx, correct? What about transform it into GP form? or yalmip?

If none of them helps, what toolbox is available?

YALMIP allows non-convex and non-DCP-compliant problems, so you can try that.

Thank you sir!! You save my time!