An inexact proximal point algorithm for maximal monotone vector fields on Hadamard manifolds

被引：28

作者：

Tang, Guo-ji ^{[1
]}

Huang, Nan-jing ^{[2
]}

机构：

[1] Guangxi Univ Nationalities, Sch Sci, Nanning 530006, Guangxi, Peoples R China

[2] Sichuan Univ, Dept Math, Chengdu 610064, Sichuan, Peoples R China

来源：

OPERATIONS RESEARCH LETTERS | 2013年 / 41卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Inexact proximal point algorithm; Hadamard manifold; Maximal monotone vector field; VARIATIONAL-INEQUALITIES; QUASI-CONVEX; ITERATIVE ALGORITHMS; PREINVEX FUNCTIONS; INVEX SETS; EXTRAGRADIENT;

D O I：

10.1016/j.orl.2013.08.003

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

In this paper, an inexact proximal point algorithm concerned with the singularity of maximal monotone vector fields is introduced and studied on Hadamard manifolds, in which a relative error tolerance with squared summable error factors is considered. It is proved that the sequence generated by the proposed method is convergent to a solution of the problem. Moreover, an application to the optimization problem on Hadamard manifolds is given. The main results presented in this paper generalize and improve some corresponding known results given in the literature. (C) 2013 Elsevier By. All rights reserved.

引用

页码：586 / 591

页数：6

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