Inexact Proximal Point Algorithms and Descent Methods in Optimization

Proximal point methods have been used by the optimization community to analyze different algorithms like multiplier methods for constrained optimization, and bundle methods for nonsmooth problems. This paper aims to be an introduction to the theory of proximal algorithms borrowing ideas from descent methods for unconstrained optimization. This new viewpoint allows us to present a simple and natural convergence proof. We also improve slightly the results from Solodov and Svaiter (1999).