First-order primal-dual methods for nonsmooth nonconvex optimisation

TL;DR

This paper reviews primal-dual algorithms for complex nonsmooth, non-convex saddle-point problems, introducing a new Bregman divergence-based analysis that simplifies convergence conditions.

Contribution

It offers a novel Bregman divergence-based analysis framework for primal-dual methods in nonsmooth non-convex optimization, enhancing understanding of their convergence.

Findings

New convergence analysis using Bregman divergences

Simplified conditions for primal-dual method convergence

Applicable to nonsmooth, non-convex saddle-point problems

Abstract

We provide an overview of primal-dual algorithms for nonsmooth and non-convex-concave saddle-point problems. This flows around a new analysis of such methods, using Bregman divergences to formulate simplified conditions for convergence.