A bregman forward-backward linesearch algorithm for nonconvex composite optimization: Superlinear convergence to nonisolated local minima

Masoud Ahookhosh, Andreas Themelis, Panagiotis Patrinos

研究成果: Contribution to journalArticle査読

2 被引用数 (Scopus)

抄録

We introduce Bella, a locally superlinearly convergent Bregman forward-backward splitting method for minimizing the sum of two nonconvex functions, one of which satisfies a relative smoothness condition and the other one is possibly nonsmooth. A key tool of our methodology is the Bregman forward-backward envelope (BFBE), an exact and continuous penalty function with favorable first- and second-order properties, which enjoys a nonlinear error bound when the objective function satisfies a Lojasiewicz-type property. The proposed algorithm is of linesearch type over the BFBE along user-defined update directions and converges subsequentially to stationary points and globally under the Kurdyka-Lojasiewicz condition. Moreover, when the update directions are superlinear in the sense of Facchinei and Pang [Finite-Dimensional Variational Inequalities and Complementarity Problems, Volume I, Springer, New York, 2003], owing to the given nonlinear error bound unit stepsize is eventually always accepted and the algorithm attains superlinear convergence rates even when the limit point is a nonisolated minimum.

本文言語英語
ページ(範囲)653-685
ページ数33
ジャーナルSIAM Journal on Optimization
31
1
DOI
出版ステータス出版済み - 2 2021

All Science Journal Classification (ASJC) codes

  • ソフトウェア
  • 理論的コンピュータサイエンス

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