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
收藏
页码：733 / 746
页数：14
相关论文
共 50 条
  • [1] Inexact Newton methods for semismooth equations with applications to variational inequality problems
    Facchinei, F
    Fischer, A
    Kanzow, C
    [J]. NONLINEAR OPTIMIZATION AND APPLICATIONS, 1996, : 125 - 139
  • [2] A semismooth Newton method for nonlinear symmetric cone programming
    Kong, Lingchen
    Meng, Qingmin
    [J]. MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 2012, 76 (02) : 129 - 145
  • [3] A semismooth Newton method for nonlinear symmetric cone programming
    Lingchen Kong
    Qingmin Meng
    [J]. Mathematical Methods of Operations Research, 2012, 76 : 129 - 145
  • [4] A nonmonotone semismooth inexact Newton method
    Bonettini, Silvia
    Tinti, Federica
    [J]. OPTIMIZATION METHODS & SOFTWARE, 2007, 22 (04): : 637 - 657
  • [5] A smoothing inexact Newton method for variational inequality problems
    Zheng, Xiuyun
    Liu, Hongwei
    [J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2011, 88 (06) : 1283 - 1293
  • [6] A smoothing inexact Newton method for variational inequalities with nonlinear constraints
    Zhili Ge
    Qin Ni
    Xin Zhang
    [J]. Journal of Inequalities and Applications, 2017
  • [7] A smoothing inexact Newton method for variational inequalities with nonlinear constraints
    Ge, Zhili
    Ni, Qin
    Zhang, Xin
    [J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2017,
  • [8] Adaptive inexact smoothing Newton method for a nonconforming discretization of a variational inequality
    Gharbia, Ibtihel Ben
    Ferzly, Joelle
    Vohralik, Martin
    Yousef, Soleiman
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2023, 133 : 12 - 29
  • [9] Extended Semismooth Newton Method for Functions with Values in a Cone
    Séverine Bernard
    Catherine Cabuzel
    Silvère Paul Nuiro
    Alain Pietrus
    [J]. Acta Applicandae Mathematicae, 2018, 155 : 85 - 98
  • [10] Extended Semismooth Newton Method for Functions with Values in a Cone
    Bernard, Severine
    Cabuzel, Catherine
    Nuiro, Silvere Paul
    Pietrus, Alain
    [J]. ACTA APPLICANDAE MATHEMATICAE, 2018, 155 (01) : 85 - 98
12345