An Accelerated Inexact Proximal Point Algorithm for Convex Minimization

Bingsheng He, Xiaoming YUAN*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)

Abstract

The proximal point algorithm is classical and popular in the community of optimization. In practice, inexact proximal point algorithms which solve the involved proximal subproblems approximately subject to certain inexact criteria are truly implementable. In this paper, we first propose an inexact proximal point algorithm with a new inexact criterion for solving convex minimization, and show its O(1/k) iteration-complexity. Then we show that this inexact proximal point algorithm is eligible for being accelerated by some influential acceleration schemes proposed by Nesterov. Accordingly, an accelerated inexact proximal point algorithm with an iteration-complexity of O(1/k 2) is proposed.

Original languageEnglish
Pages (from-to)536-548
Number of pages13
JournalJournal of Optimization Theory and Applications
Volume154
Issue number2
DOIs
Publication statusPublished - Aug 2012

Scopus Subject Areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

User-Defined Keywords

  • Acceleration
  • Convex minimization
  • Inexact
  • Proximal point algorithm

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