Title: Hidden convexity in nonconvex optimization.
Abstract: In nonconvex optimization, not only the objective but even the feasible set may lack convexity. It may seem therefore that the concepts and methodology of convex optimization can no longer have a fundamental role, but this is actually wrong. Standard sufficient conditions for local optimality in nonlinear programming and its extensions turn out to correspond to characterizing optimality in terms of a local convex-concave-type saddle point of an augmented Lagrangian function. Algorithms that effectively in both primal and dual elements are thereby revealed as working just as they would in the convex case.