The proximal point method revisited

2017/12/17 by Drusvyatskiy, Dmitriy · 5 citations
#65K05 #90C06 #90C25 #90C30 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1712.06038

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.

Cited by

• A Proximal Method for Composite Optimization with Smooth and Convex Components
• An accelerated proximal bundle method for convex optimization
• Verification of Sequential Convex Programming for Parametric Non-convex Optimization
• The Potential of Second-Order Optimization for LLMs: A Study with Full Gauss-Newton
• A Simple Adaptive Proximal Gradient Method for Nonconvex Optimization

Related

• The Ball-Proximal (="Broximal") Point Method: a New Algorithm, Convergence Theory, and Applications
• RECAPP: Crafting a More Efficient Catalyst for Convex Optimization
• A Unified Theory of Stochastic Proximal Point Methods without Smoothness
• Understanding Nesterov's Acceleration via Proximal Point Method
• Un-regularizing: approximate proximal point and faster stochastic\n algorithms for empirical risk minimization