I have devised some function that I wish to minimize. Overall the function is not convex, but it is so on the relevant constraint set of its arguments (which is also convex). My question is now whether the overall nonconvexity of the function may render the whole problem a nonconvex one, despite the fact that optimization takes place only in some convex domain where the function is also convex. My intuition say that this shouldn’t pose a problem, but I am lacking a strict argument, let alone a proof.
any help is appreciated…
If you define your function only on the convex set of relevant arguments, then it will be a convex function, regardless of possible extensions outside this set. Methods for minimizing convex functions on convex sets will then work as advertised.