ITERATIVE ALGORITHMS FOR EQUILIBRIUM PROBLEMS BASED ON PROXIMAL-LIKE METHODS

被引：0
|
作者：
Bao, J. F. [1 ]
Fang, D. H. [2 ]
Li, C. [1 ]
机构：
[1] Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China
[2] Jishou Univ, Coll Math & Stat, Jishou 416000, Peoples R China
来源：
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS | 2014年 / 15卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Equilibrium problems; projection method; error bound; linear convergence; ERROR-BOUNDS; SYSTEMS; CONVERGENCE; INEQUALITY; EXISTENCE;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we present two algorithms, namely Algorithm 1.2 and Algorithm 1.3, with most violated constraint control strategy used in the projection method for solving equilibrium problems. Compared with the projection methods, both algorithms are designed to avoid computing the projection to the nonlinear level set. Under certain conditions, the convergences of the Algorithm 1.2 and Algorithm 1.3 are established, and the linear convergence rate of Algorithm 1.3 is obtained. At last, some examples to illustrate the convergence performance of Algorithm 1.2 and Algorithm 1.3 are given.
引用
收藏
页码：89 / 104
页数：16
相关论文
共 50 条
  • [1] Equilibrium programming using proximal-like algorithms
    Flam, SD
    Antipin, AS
    MATHEMATICAL PROGRAMMING, 1997, 78 (01) : 29 - 41
  • [2] Proximal-like algorithms for equilibrium seeking in mixed-integer Nash equilibrium problems
    Fabiani, Filippo
    Franci, Barbara
    Sagratella, Simone
    Schmidt, Martin
    Staudigl, Mathias
    2022 IEEE 61ST CONFERENCE ON DECISION AND CONTROL (CDC), 2022, : 4137 - 4142
  • [3] Proximal-like methods for convex minimization problems
    Kanzow, C
    OPTIMIZATION AND CONTROL WITH APPLICATIONS, 2005, 96 : 369 - 392
  • [4] Convergence of proximal-like algorithms
    Teboulle, M
    SIAM JOURNAL ON OPTIMIZATION, 1997, 7 (04) : 1069 - 1083
  • [5] Modified proximal-like extragradient methods for two classes of equilibrium problems in Hilbert spaces with applications
    Rehman, Habib ur
    Kumam, Poom
    Argyros, Ioannis K.
    Alreshidi, Nasser Aedh
    Computational and Applied Mathematics, 2021, 40 (02)
  • [6] Modified proximal-like extragradient methods for two classes of equilibrium problems in Hilbert spaces with applications
    Habib ur Rehman
    Poom Kumam
    Ioannis K. Argyros
    Nasser Aedh Alreshidi
    Computational and Applied Mathematics, 2021, 40
  • [7] Modified proximal-like extragradient methods for two classes of equilibrium problems in Hilbert spaces with applications
    Rehman, Habib Ur
    Kumam, Poom
    Argyros, Ioannis K.
    Alreshidi, Nasser Aedh
    COMPUTATIONAL & APPLIED MATHEMATICS, 2021, 40 (02):
  • [8] Three novel two-step proximal-like methods for solving equilibrium and fixed point problems in real Hilbert spaces
    Kanikar Muangchoo
    Computational and Applied Mathematics, 2022, 41
  • [9] Three novel two-step proximal-like methods for solving equilibrium and fixed point problems in real Hilbert spaces
    Muangchoo, Kanikar
    COMPUTATIONAL & APPLIED MATHEMATICS, 2022, 41 (08):
  • [10] Nonlinear rescaling and proximal-like methods in convex optimization
    Polyak, R
    Teboulle, M
    MATHEMATICAL PROGRAMMING, 1997, 76 (02) : 265 - 284
12345