An approximate proximal-extragradient type method for monotone variational inequalities

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:300

Article

He, BS ; Yang, ZH ; Yuan, XM

关键词: monotone variational inequality;    inexact proximal point algorithm;   

DOI  :  10.1016/j.jmaa.2004.04.068

来源: Elsevier

【 摘 要 】

Proximal point algorithms (PPA) are attractive methods for monotone variational inequalities. The approximate versions of PPA are more applicable in practice. A modified approximate proximal point algorithm (APPA) presented by Solodov and Svaiter [Math. Programming, Ser. B 88 (2000) 371-389] relaxes the inexactness criterion significantly. This paper presents an extended version of Solodov-Svaiter's APPA. Building the direction from current iterate to the new iterate obtained by Solodov-Svaiter's APPA, the proposed method improves the profit at each iteration by choosing the optimal step length along this direction. In addition, the inexactness restriction is relaxed further. Numerical example indicates the improvement of the proposed method. (C) 2004 Elsevier Inc. All rights reserved.

【 授权许可】

Free