Local Linear Convergence of an Outer Approximation Projection Method for Variational Inequalities

被引：0

作者：

Lu, Shu ^{[1
]}

Singh, Sudhanshu ^{[1
]}

机构：

[1] Univ N Carolina, Dept Stat & Operat Res, Chapel Hill, NC 27599 USA

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2011年 / 151卷 / 01期

基金：

美国国家科学基金会;

关键词：

Variational inequality; Projection method; Outer approximation; Local convergence; ALGORITHM;

D O I：

10.1007/s10957-011-9873-8

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：

This paper considers an outer approximation projection method for variational inequalities, in which the projections are not performed on the original set that appears in the variational inequality, but on a polyhedral convex set defined by the linearized constraints. It shows that the method converges linearly, when the starting point is sufficiently close to the solution and the step lengths are sufficiently small.

引用

页码：52 / 63

页数：12

共 50 条

[21] DYNAMIC STOCHASTIC VARIATIONAL INEQUALITIES AND CONVERGENCE OF DISCRETE APPROXIMATION
Chen, Xiaojun
Shen, Jinglai
SIAM JOURNAL ON OPTIMIZATION, 2022, 32 (04) : 2909 - 2937
[22] Strong Convergence of a Projection-Type Method for Mixed Variational Inequalities in Hilbert Spaces
Tang, Guo-ji
Wan, Zhongping
Huang, Nan-jing
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2018, 39 (11) : 1103 - 1119
[23] Weak convergence of a projection algorithm for variational inequalities in a Banach space
Iiduka, Hideaki
Takahashi, Wataru
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 339 (01) : 668 - 679
[24] Outer approximation methods for solving variational inequalities in Hilbert space
Gibali, Aviv
Reich, Simeon
Zalas, Rafal
OPTIMIZATION, 2017, 66 (03) : 417 - 437
[25] PROJECTION METHODS IN NON-LINEAR VARIATIONAL INEQUALITIES
GAJEWSKI, H
KLUGE, R
MATHEMATISCHE NACHRICHTEN, 1970, 46 (1-6) : 363 - &
[26] A modified projection method for monotone variational inequalities
Noor, MA
APPLIED MATHEMATICS LETTERS, 1999, 12 (05) : 83 - 87
[27] MODIFIED PROJECTION METHOD FOR GENERAL VARIATIONAL INEQUALITIES
Bnouhachem, Abdellah
Noor, Muhammad Aslam
Sheng Zhaohan
INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 2011, 25 (27): : 3595 - 3610
[28] A Relaxed Projection Method for Split Variational Inequalities
He, Hongjin
Ling, Chen
Xu, Hong-Kun
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2015, 166 (01) : 213 - 233
[29] A projection descent method for solving variational inequalities
Abdellah Bnouhachem
Qamrul Hasan Ansari
Ching-Feng Wen
Journal of Inequalities and Applications, 2015
[30] An Infeasible Stochastic Approximation and Projection Algorithm for Stochastic Variational Inequalities
Zhang, Xiao-Juan
Du, Xue-Wu
Yang, Zhen-Ping
Lin, Gui-Hua
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2019, 183 (03) : 1053 - 1076

← 1 2 3 4 5 →