Strong Convergence of a Modified Extragradient Method to the Minimum-Norm Solution of Variational Inequalities

被引:39
|
作者
Yao, Yonghong [1 ]
Noor, Muhammad Aslam [2 ,3 ]
Liou, Yeong-Cheng [4 ]
机构
[1] Tianjin Polytech Univ, Dept Math, Tianjin 300387, Peoples R China
[2] COMSATS Inst Informat Technol, Dept Math, Islamabad 44000, Pakistan
[3] King Saud Univ, Coll Sci, Dept Math, Riyadh 11451, Saudi Arabia
[4] Cheng Shiu Univ, Dept Informat Management, Kaohsiung 833, Taiwan
关键词
STEEPEST-DESCENT METHODS; NONEXPANSIVE-MAPPINGS; MONOTONE-OPERATORS; ITERATIVE METHODS; 3-STEP ITERATIONS; WEAK-CONVERGENCE; HILBERT-SPACE; ALGORITHMS;
D O I
10.1155/2012/817436
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We suggest and analyze a modified extragradient method for solving variational inequalities, which is convergent strongly to the minimum-norm solution of some variational inequality in an infinite-dimensional Hilbert space.
引用
收藏
页数:9
相关论文
共 50 条
  • [1] A modified Korpelevich's method convergent to the minimum-norm solution of a variational inequality
    Yao, Yonghong
    Marino, Giuseppe
    Muglia, Luigi
    OPTIMIZATION, 2014, 63 (04) : 559 - 569
  • [2] ADAPTIVE INERTIAL SUBGRADIENT EXTRAGRADIENT METHODS FOR FINDING MINIMUM-NORM SOLUTIONS OF PSEUDOMONOTONE VARIATIONAL INEQUALITIES
    Tan, Bing
    LI, Songxiao
    JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION, 2023, 19 (10) : 7640 - 7659
  • [3] Strong and linear convergence of projection-type method with an inertial term for finding minimum-norm solutions of pseudomonotone variational inequalities in Hilbert spaces
    Duong Viet Thong
    Li, Xiaoxiao
    Dong, Qiao-Li
    Vu Tien Dung
    Nguyen Phuong Lan
    NUMERICAL ALGORITHMS, 2023, 92 (04) : 2243 - 2274
  • [4] Modified inertial extragradient methods for finding minimum-norm solution of the variational inequality problem with applications to optimal control problem
    Tan, Bing
    Sunthrayuth, Pongsakorn
    Cholamjiak, Prasit
    Je Cho, Yeol
    INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2023, 100 (03) : 525 - 545
  • [5] Convergence of the Modified Extragradient Method for Variational Inequalities with Non-Lipschitz Operators
    Denisov S.V.
    Semenov V.V.
    Chabak L.M.
    Cybernetics and Systems Analysis, 2015, 51 (05) : 757 - 765
  • [6] Strong convergence of the Halpern subgradient extragradient method for solving variational inequalities in Banach spaces
    Liu, Ying
    JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2017, 10 (02): : 395 - 409
  • [7] EXTRAGRADIENT METHOD FOR VARIATIONAL INEQUALITIES
    Bnouhachem, Abdellah
    Noor, Muhammad Aslam
    Al-Said, Eisa
    Khalfaoui, Mohamed
    Sheng Zhaohan
    HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, 2011, 40 (06): : 839 - 854
  • [8] A modified subgradient extragradient method for solving monotone variational inequalities
    He, Songnian
    Wu, Tao
    JOURNAL OF INEQUALITIES AND APPLICATIONS, 2017,
  • [9] WEAK CONVERGENCE THEOREM BY A MODIFIED EXTRAGRADIENT METHOD FOR VARIATIONAL INCLUSIONS,VARIATIONAL INEQUALITIES AND FIXED POINT PROBLEMS
    Ceng, Lu-Chuan
    Guu, Sy-Ming
    Yao, Jen-Chih
    JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2013, 14 (01) : 21 - 31
  • [10] Strong Convergence of an Inertial Extragradient Method with an Adaptive Nondecreasing Step Size for Solving Variational Inequalities
    Linh, Nguyen Xuan
    Thong, Duong Viet
    Cholamjiak, Prasit
    Tuan, Pham Anh
    Van Long, Luong
    ACTA MATHEMATICA SCIENTIA, 2022, 42 (02) : 795 - 812