Douglas–Rachford splitting and ADMM for nonconvex optimization: Tight convergence results

Andreas Themelis, Panagiotis Patrinos

研究成果: Contribution to journalArticle査読

15 被引用数 (Scopus)

抄録

Although originally designed and analyzed for convex problems, the alternating direction method of multipliers (ADMM) and its close relatives, Douglas–Rachford splitting (DRS) and Peaceman–Rachford splitting (PRS), have been observed to perform remarkably well when applied to certain classes of structured nonconvex optimization problems. However, partial global convergence results in the nonconvex setting have only recently emerged. In this paper we show how the Douglas–Rachford envelope, introduced in 2014, can be employed to unify and considerably simplify the theory for devising global convergence guarantees for ADMM, DRS, and PRS applied to nonconvex problems under less restrictive conditions, larger prox-stepsizes, and overrelaxation parameters than previously known. In fact, our bounds are tight whenever the overrelaxation parameter ranges in (0, 2]. The analysis of ADMM uses a universal primal equivalence with DRS that generalizes the known duality of the algorithms.

本文言語英語
ページ(範囲)149-181
ページ数33
ジャーナルSIAM Journal on Optimization
30
1
DOI
出版ステータス出版済み - 2020
外部発表はい

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

フィンガープリント

「Douglas–Rachford splitting and ADMM for nonconvex optimization: Tight convergence results」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル