The proximal point method revisited

TL;DR

This paper reviews the proximal point method's role in large-scale optimization, highlighting recent advances like subgradient methods, prox-linear algorithms, and Catalyst acceleration for empirical risk minimization.

Contribution

It provides a concise survey of recent developments and applications of the proximal point method in various large-scale optimization contexts.

Findings

Proximally guided subgradient methods improve stochastic approximation.

Prox-linear algorithms effectively minimize compositions of convex functions.

Catalyst acceleration enhances regularized empirical risk minimization.

Abstract

In this short survey, I revisit the role of the proximal point method in large scale optimization. I focus on three recent examples: a proximally guided subgradient method for weakly convex stochastic approximation, the prox-linear algorithm for minimizing compositions of convex functions and smooth maps, and Catalyst generic acceleration for regularized Empirical Risk Minimization.