Reviews: An Inexact Augmented Lagrangian Framework for Nonconvex Optimization with Nonlinear Constraints

This paper uses the Augmented Lagrangian method to solve optimization problems for a sum of functions f and g, where f is nonconvex and g is convex but'proximal-friendly' subject to quite general nonlinear constraints. The proposed method solves the primal problem within some error epsilon_k that is gradually decreased as a penalty schedule beta_k is increasing across iterations. The approximate intermediate problems are solved using first order and second order solvers. The proposed analysis is technically non-trivial and interesting. The presentation of the paper was poor and at times confusing which made this a borderline paper.