I know equality constraint exp(x)+exp(y)+exp(z)==1 is not convex. Do you have any idea to address it?
Nonlinear equality constraints are non-convex.
exp(x)+exp(y)+exp(z)<=1 is convex and can be entered in CVX. If you solve this relaxed problem, and it turns out that equality holds, then you have a solution to the original (equality-constrained) problem. Otherwise, you don’t.
If the relaxation doesn’t provide a solution to the original problem, use a non-convex solver, such as available under YALMIP.
Thank you for your comment. However, if I set exp(x)+exp(y)+exp(z)<=1, the equality is not hold. I should make it convex, so non-convex solver is not suitable for my situation. Thanks again!
Use a non-convex solver, change your model to be convex. or abandon the problem. The choice is yours.
Exactly, Mark. Thank you for your suggestion and I will change my model. Have a good day.