Peeling off a nonconvex cover of an actual convex problem: Hidden convexity

Convexity is, without a doubt, one of the most desirable features in optimization. Many optimization problems that are nonconvex in their original settings may become convex after performing certain equivalent transformations. This paper studies the conditions for such hidden convexity. More specifically, some transformation-independent sufficient conditions have been derived for identifying hidden convexity. The derived sufficient conditions are readily verifiable for quadratic optimization problems. The global minimizer of a hidden convex programming problem can be identified using a local search algorithm.