Formulating a problem as a convex optimization problem usually implicitly considered to imply being able to find global minimizer of the objective. My question is that if it is true or not.
Generally speaking, I wonder when minimizing a convex objective is tractable and when it is not tractable?
In particular, suppose we have a convex function $f$, and need a polynomial time algorithm to find its minimum. Does convexity alone guarantee existence of such an algorithm (I guess not) or more conditions are needed?
(It is a surprise to me why this very basic question is not explicitly addressed in many relevant texts.)