AN INEXACT SEMISMOOTH NEWTON METHOD FOR VARIATIONAL INEQUALITY WITH SYMMETRIC CONE CONSTRAINTS

被引：2

作者：

Chen, Shuang ^{[1
]}

Pang, Li-Ping ^{[1
]}

Li, Dan ^{[2
]}

机构：

[1] Dalian Univ Technol, Sch Math Sci, Dalian 116024, Liaoning, Peoples R China

[2] Dalian Univ, Informat & Engn Coll, Dalian 116622, Peoples R China

来源：

JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION | 2015年 / 11卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Variational inequality; symmetric cone; Newton method; semismooth; Jordan algebra;

D O I：

10.3934/jimo.2015.11.733

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this paper, we consider using the inexact nonsmooth Newton method to efficiently solve the symmetric cone constrained variational inequality (VISCC) problem. It red provides a unified framework for dealing with the variational inequality with nonlinear constraints, variational inequality with the second-order cone constraints, and the variational inequality with semidefinite cone constraints. We get convergence of the above method and apply the results to three special types symmetric cones.

引用

页码：733 / 746

页数：14

共 50 条

[31] Path-following and semismooth Newton methods for the variational inequality arising from two membranes problem
Zhang, Shougui
Yan, Yueyue
Ran, Ruisheng
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2019, 2019 (1)
[32] Path-following and semismooth Newton methods for the variational inequality arising from two membranes problem
Shougui Zhang
Yueyue Yan
Ruisheng Ran
Journal of Inequalities and Applications, 2019
[33] A REGULARIZED INEXACT SMOOTHING NEWTON METHOD FOR CIRCULAR CONE COMPLEMENTARITY PROBLEM
Chi, Xiaoni
Tao, Jiyuan
Zhu, Zhibin
Duan, Fujian
PACIFIC JOURNAL OF OPTIMIZATION, 2017, 13 (02): : 197 - 218
[34] Inexact Newton method for non-linear functions with values in a cone
Ferreira, O. P.
Silva, G. N.
APPLICABLE ANALYSIS, 2019, 98 (08) : 1461 - 1477
[35] A globally and locally superlinearly convergent inexact Newton-GMRES method for large-scale variational inequality problem
Rui, Shaoping
Xu, Chengxian
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2014, 91 (03) : 578 - 587
[36] A superlinearly convergent Newton-like algorithm for variational inequality problems with inequality constraints
Liping Zhang
Yanlian Lai
Mathematical Methods of Operations Research, 2000, 51 : 459 - 470
[37] A smoothing projected Newton-type method for semismooth equations with bound constraints
Tong, Xiaojiao
Zhou, Shuzi
JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION, 2005, 1 (02) : 235 - 250
[38] A superlinearly convergent Newton-like algorithm for variational inequality problems with inequality constraints
Zhang, LP
Lai, YL
MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 2000, 51 (03) : 459 - 470
[39] An Inexact Semismooth Newton Method on Riemannian Manifolds with Application to Duality-Based Total Variation Denoising
Diepeveen, Willem
Lellmann, Jan
SIAM JOURNAL ON IMAGING SCIENCES, 2021, 14 (04): : 1565 - 1600
[40] Higher Order Variational Symmetric Duality Over Cone Constraints
Khatri, Sony
Prasad, Ashish Kumar
MATHEMATICS AND COMPUTING, ICMC 2022, 2022, 415 : 453 - 464

← 1 2 3 4 5 →