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

Puya Latafat, Andreas Themelis, Panagiotis Patrinos

研究成果: ジャーナルへの寄稿学術誌査読

抄録

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.

本文言語英語
ページ(範囲)195-224
ページ数30
ジャーナルMathematical Programming
193
1
DOI
出版ステータス出版済み - 5月 2022

!!!All Science Journal Classification (ASJC) codes

  • ソフトウェア
  • 数学 (全般)

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