Terry Rockafellar

Hidden convexity in nonconvex optimization

Terry Rockafellar
University of Washington

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.