In this talk, we discuss about an inexact proximal augmented Lagrangian IPAL method for solving nonconvex composite optimization problems with nonlinear K-convex constraints, i.e., the constraints are convex with respect to the partial order given by a closed convex cone K. Each iteration of this scheme consists of inexactly solving a proximal augmented Lagrangian subproblem by an accelerated composite gradient algorithm followed by a Lagrange multiplier update. Under some mild assumptions, it is shown that IPAL generates an approximate stationary solution of the constrained problem in O(1/eps^3) inner iterations, where eps>0 is a given tolerance. Some numerical experiments to illustrate the computational efficiency of the proposed method will be presented.

This is a joint work with Renato D.C. Monteiro and Weiwei Kong - Georgia Tech/USA