ON THE CONVERGENCE OF INEXACT PROXIMAL POINT ALGORITHM ON HADAMARD MANIFOLDS

被引：14

作者：

Ahmadi, P. ^{[1
]}

Khatibzadeh, H. ^{[1
]}

机构：

[1] Univ Zanjan, Dept Math, Zanjan, Iran

来源：

TAIWANESE JOURNAL OF MATHEMATICS | 2014年 / 18卷 / 02期

关键词：

MONOTONE VECTOR-FIELDS; OPERATORS;

D O I：

10.11650/tjm.18.2014.3066

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we consider the proximal point algorithm to approximate a singularity of a multivalued monotone vector field on a Hadamard manifold. We study the convergence of the sequence generated by an inexact form of the algorithm. Our results extend the results of [3, 25] to Hadamard manifolds as well as the main result of [11] with more general assumptions on the control sequence. We also give some application to optimization.

引用

收藏

页码：419 / 433

页数：15

相关论文

共 29 条

[1]

[Anonymous], 1996, TRANSLATIONS MATH MO

[2] Local convergence of the proximal point method for a special class of nonconvex functions on Hadamard manifolds [J].

Bento, G. C. ;

Ferreira, O. P. ;

Oliveira, P. R. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 73 (02) :564-572

[3]

Bento G. C., 2012, OPTIMIZATION, P1

[4] INFINITE PRODUCTS OF RESOLVENTS [J].

BREZIS, H ;

LIONS, PL .

ISRAEL JOURNAL OF MATHEMATICS, 1978, 29 (04) :329-345

[5] MULTI-VALUED MONOTONE NONLINEAR MAPPINGS AND DUALITY MAPPINGS IN BANACH SPACES [J].

BROWDER, FE .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1965, 118 (06) :338-&

[6] Iterative Approaches to Find Zeros of Maximal Monotone Operators by Hybrid Approximate Proximal Point Methods [J].

Ceng, Lu Chuan ;

Liou, Yeong Cheng ;

Naraghirad, Eskandar .

FIXED POINT THEORY AND APPLICATIONS, 2011,

[7] Convex- and monotone-transformable mathematical programming problems and a proximal-like point method [J].

Da Cruz Neto, J. X. ;

Ferreira, O. P. ;

Perez, L. R. Lucambio ;

Nemeth, S. Z. .

JOURNAL OF GLOBAL OPTIMIZATION, 2006, 35 (01) :53-69

[8]

Da Cruz Neto JX., 2000, Balk. J. Geom. Appl, V5, P69

[9] Singularities of monotone vector fields and an extragradient-type algorithm [J].

Ferreira, OP ;

Pérez, LRL ;

Németh, SZ .

JOURNAL OF GLOBAL OPTIMIZATION, 2005, 31 (01) :133-151

[10] Proximal point algorithm on Riemannian manifolds [J].

Ferreira, OP ;

Oliveira, PR .

OPTIMIZATION, 2002, 51 (02) :257-270