A PROXIMAL POINT-TYPE ALGORITHM FOR PSEUDOMONOTONE EQUILIBRIUM PROBLEMS

被引：10
|
作者：
Kim, Jong Kyu [1 ]
Anh, Pham Ngoc [1 ]
Hyun, Ho Geun [1 ]
机构：
[1] Kyungnam Univ, Dept Math Educ, Masan 631701, South Korea
来源：
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY | 2012年 / 49卷 / 04期
关键词：
equilibrium problems; proximal point algorithm; pseudomonotonicity; linear proximal function; Banach contraction method; VARIATIONAL-INEQUALITIES; COMPLEMENTARITY-PROBLEMS; PRINCIPLE;
D O I：
10.4134/BKMS.2012.49.4.749
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A globally convergent algorithm for solving equilibrium problems is proposed. The algorithm is based on a proximal point algorithm (shortly (PPA)) with a positive definite matrix M which is not necessarily symmetric. The proximal function in existing (PPA) usually is the gradient of a quadratic function, namely, del(parallel to x parallel to(2)(M)). This leads to a proximal point-type algorithm. We first solve pseudomonotone equilibrium problems without Lipschitzian assumption and prove the convergence of algorithms. Next, we couple this technique with the Banach contraction method for multivalued variational inequalities. Finally some computational results are given.
引用
收藏
页码：749 / 759
页数：11
相关论文
共 50 条
  • [31] A new iterative algorithm of pseudomonotone mappings for equilibrium problems in Hilbert spaces
    Kim, Jong Kyu
    Lim, Won Hee
    JOURNAL OF INEQUALITIES AND APPLICATIONS, 2013,
  • [32] An Adapted Proximal Point Algorithm Utilizing the Golden Ratio Technique for Solving Equilibrium Problems in Banach Spaces
    Abass, Hammed Anuoluwapo
    Oyewole, Olawale Kazeem
    Moshokoa, Seithuti Philemon
    Adamu, Abubakar
    MATHEMATICS, 2024, 12 (23)
  • [33] A proximal point algorithm for minimax problems
    Achiya Dax
    BIT Numerical Mathematics, 1997, 37 : 600 - 622
  • [34] A proximal point algorithm for minimax problems
    Dax, A
    BIT, 1997, 37 (03): : 600 - 622
  • [35] An Armijo-type method for pseudomonotone equilibrium problems and its applications
    P. N. Anh
    H. A. Le Thi
    Journal of Global Optimization, 2013, 57 : 803 - 820
  • [36] The subgradient extragradient method extended to pseudomonotone equilibrium problems and fixed point problems in Hilbert space
    Yang, Jun
    Liu, Hongwei
    OPTIMIZATION LETTERS, 2020, 14 (07) : 1803 - 1816
  • [37] The subgradient extragradient method extended to pseudomonotone equilibrium problems and fixed point problems in Hilbert space
    Jun Yang
    Hongwei Liu
    Optimization Letters, 2020, 14 : 1803 - 1816
  • [38] COMMON SOLUTIONS TO PSEUDOMONOTONE EQUILIBRIUM PROBLEMS
    Hieu, D. V.
    BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2016, 42 (05) : 1207 - 1219
  • [39] Strong convergence of inertial subgradient extragradient algorithm for solving pseudomonotone equilibrium problems
    Thong, Duong Viet
    Cholamjiak, Prasit
    Rassias, Michael T.
    Cho, Yeol Je
    OPTIMIZATION LETTERS, 2022, 16 (02) : 545 - 573
  • [40] Strong convergence of inertial subgradient extragradient algorithm for solving pseudomonotone equilibrium problems
    Duong Viet Thong
    Prasit Cholamjiak
    Michael T. Rassias
    Yeol Je Cho
    Optimization Letters, 2022, 16 : 545 - 573
12345