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An Accelerated Inexact Proximal Point Algorithm for Convex Minimization

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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.

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Authors and Affiliations

  1. Department of Mathematics and National Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, 210093, China

    Bingsheng He

  2. Department of Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong, China

    Xiaoming Yuan

Authors
  1. Bingsheng He
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  2. Xiaoming Yuan
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Correspondence to Xiaoming Yuan.

Additional information

Communicated by Jen-Chih Yao.

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He, B., Yuan, X. An Accelerated Inexact Proximal Point Algorithm for Convex Minimization. J Optim Theory Appl 154, 536–548 (2012). https://doi.org/10.1007/s10957-011-9948-6

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  • DOI: https://doi.org/10.1007/s10957-011-9948-6

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