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Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

An accelerated inexact proximal point algorithm for convex minimization

Language

English

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. © 2011 Springer Science+Business Media, LLC.

Keywords

Acceleration, Convex minimization, Inexact, Proximal point algorithm

Publication Date

2012

Source Publication Title

Journal of Optimization Theory and Applications

Volume

154

Issue

2

Start Page

536

End Page

548

Publisher

Springer Verlag

ISSN (print)

00223239

ISSN (electronic)

15732878

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