Regularization Proximal Method for Monotone Variational Inclusions

被引：4

作者：

Van Hieu, Dang ^{[1
]}

Anh, Pham Ky ^{[2
]}

Ha, Nguyen Hai ^{[3
]}

机构：

[1] Thang Long Univ, TIMAS, Hanoi, Vietnam

[2] Vietnam Natl Univ, Dept Math, Hanoi, Vietnam

[3] Univ Transport & Commun, Fac Basic Sci, Hanoi, Vietnam

来源：

NETWORKS & SPATIAL ECONOMICS | 2021年 / 21卷 / 04期

关键词：

Variational inclusion; Iterative method; Regularization; Monotonicity; BACKWARD SPLITTING METHOD; CONTRACTION METHODS; PROJECTION; ALGORITHM; EXTRAGRADIENT; INEQUALITIES; OPERATORS;

D O I：

10.1007/s11067-021-09552-7

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：

The paper concerns with a new iterative method for solving a monotone variational inclusion problem in a Hilbert space. The method is of the proximal contraction type incorporated with the regularization technique. Under the prediction stepsize conditions, we establish the strong convergence of the iterative sequences generated by the method to a particular solution of the problem satisfying a variational inequality problem. Finally, we give some numerical examples to illustrate the behavior of the new method in comparison with existing ones.

引用

页码：905 / 932

页数：28

共 50 条

[21] Proximal algorithm for solving monotone variational inclusion
Zhang, Cuijie
Wang, Yinan
OPTIMIZATION, 2018, 67 (08) : 1197 - 1209
[22] An improved proximal-based decomposition method for structured monotone variational inequalities
Li Min
Yuan Xiao-ming
APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION, 2007, 28 (12) : 1659 - 1668
[23] An improved proximal alternating direction method for monotone variational inequalities with separable structure
Xiaoming Yuan
Computational Optimization and Applications, 2011, 49 : 17 - 29
[24] A subgradient proximal method for solving a class of monotone multivalued variational inequality problems
P.N. Anh
T.V. Thang
H.T.C. Thach
Numerical Algorithms, 2022, 89 : 409 - 430
[25] An improved proximal-based decomposition method for structured monotone variational inequalities
Min Li
Xiao-ming Yuan
Applied Mathematics and Mechanics, 2007, 28 : 1659 - 1668
[26] An improved proximal-based decomposition method for structured monotone variational inequalities
李敏
袁晓明
Applied Mathematics and Mechanics(English Edition), 2007, (12) : 1659 - 1668
[27] A subgradient proximal method for solving a class of monotone multivalued variational inequality problems
Anh, P. N.
Thang, T. V.
Thach, H. T. C.
NUMERICAL ALGORITHMS, 2022, 89 (01) : 409 - 430
[28] An improved proximal alternating direction method for monotone variational inequalities with separable structure
Yuan, Xiaoming
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2011, 49 (01) : 17 - 29
[29] REGULARIZATION AND ITERATION METHODS FOR A CLASS OF MONOTONE VARIATIONAL INEQUALITIES
Chen, Rudong
Su, Yongfu
Xu, Hong-Kun
TAIWANESE JOURNAL OF MATHEMATICS, 2009, 13 (2B): : 739 - 752
[30] Regularization method for Noor’s variational inequality problem induced by a hemicontinuous monotone operator
Yeol Je Cho
Narin Petrot
Fixed Point Theory and Applications, 2012

← 1 2 3 4 5 →