In the optimization problem, both objective function and the constraint functions are non-convex. (topology optimization)
- objective function: force on structure
- constraint functions: material volumes
However, I can transform the non-convex constraint function to be convex. The modified constraint function is not the same in the function shape, but it has the same physical meaning in convergence.
I thought that it find better solutions with convex constraint function, but in my case, the problems with non-convex constraints find better solutions ('better' means the number of local optimum solutions with different initial values).
I think I can arrange the question as follow, "Is it guarantee that I can find better solutions in the optimization problem has a non-convex objective function with convex constraint function than with non-convex constraint function? (assume the meaning of the convex/non-convex constraint functions are the same)"