Block-coordinate and incremental aggregated proximal gradient methods for nonsmooth nonconvex problems

Puya Latafat, Andreas Themelis, Panagiotis Patrinos

Research output: Contribution to journalArticlepeer-review

Abstract

This paper analyzes block-coordinate proximal gradient methods for minimizing the sum of a separable smooth function and a (nonseparable) nonsmooth function, both of which are allowed to be nonconvex. The main tool in our analysis is the forward-backward envelope, which serves as a particularly suitable continuous and real-valued Lyapunov function. Global and linear convergence results are established when the cost function satisfies the Kurdyka–Łojasiewicz property without imposing convexity requirements on the smooth function. Two prominent special cases of the investigated setting are regularized finite sum minimization and the sharing problem; in particular, an immediate byproduct of our analysis leads to novel convergence results and rates for the popular Finito/MISO algorithm in the nonsmooth and nonconvex setting with very general sampling strategies.

Original languageEnglish
JournalMathematical Programming
DOIs
Publication statusAccepted/In press - 2021

All Science Journal Classification (ASJC) codes

  • Software
  • Mathematics(all)

Fingerprint Dive into the research topics of 'Block-coordinate and incremental aggregated proximal gradient methods for nonsmooth nonconvex problems'. Together they form a unique fingerprint.

Cite this