The forward-backward splitting method for finding the minimum like-norm solution of the mixed variational inequality problem

被引：0
作者：
Guan, Wei-Bo [1 ]
Song, Wen [1 ]
机构：
[1] Harbin Normal Univ, Sch Math Sci, Harbin 150025, Peoples R China
来源：
JOURNAL OF INEQUALITIES AND APPLICATIONS | 2023年 / 2023卷 / 01期
关键词：
Mixed variational inequality problem; Forward-backward splitting method; Minimum like-norm solution; Regularization; EXISTENCE;
D O I：
10.1186/s13660-023-03039-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider a general class of convex optimization problems in which one seeks to minimize a strongly convex function over a closed and convex set, which is by itself an optimal set of another mixed variational inequality problem in a Hilbert space. Regularized forward-backward splitting method is applied to find the minimum like-norm solution of the mixed variational inequality problem under investigation.
引用
收藏
页数：18
相关论文
共 21 条
  • [1] Albert Y., 2006, Nonlinear Ill-Posed Problems of Monotone Type
  • [2] A first order method for finding minimal norm-like solutions of convex optimization problems
    Beck, Amir
    Sabach, Shoham
    [J]. MATHEMATICAL PROGRAMMING, 2014, 147 (1-2) : 25 - 46
  • [3] A GENERAL INERTIAL PROXIMAL POINT ALGORITHM FOR MIXED VARIATIONAL INEQUALITY PROBLEM
    Chen, Caihua
    Ma, Shiqian
    Yang, Junfeng
    [J]. SIAM JOURNAL ON OPTIMIZATION, 2015, 25 (04) : 2120 - 2142
  • [4] Signal recovery by proximal forward-backward splitting
    Combettes, PL
    Wajs, VR
    [J]. MULTISCALE MODELING & SIMULATION, 2005, 4 (04) : 1168 - 1200
  • [5] FINITE PERTURBATION OF CONVEX-PROGRAMS
    FERRIS, MC
    MANGASARIAN, OL
    [J]. APPLIED MATHEMATICS AND OPTIMIZATION, 1991, 23 (03) : 263 - 273
  • [6] Existence and uniqueness for a linear mixed variational inequality arising in electrical circuits with transistors
    Goeleven, D.
    [J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2008, 138 (03) : 397 - 406
  • [7] Konnov I.V., 2002, J. Appl. Math, V2, P289, DOI DOI 10.1155/S1110757X02106012
  • [8] Analysis of two variants of an inertial projection algorithm for finding the minimum-norm solutions of variational inequality and fixed point problems
    Linh, Ha Manh
    Reich, Simeon
    Thong, Duong Viet
    Dung, Vu Tien
    Lan, Nguyen Phuong
    [J]. NUMERICAL ALGORITHMS, 2022, 89 (04) : 1695 - 1721
  • [9] SPLITTING ALGORITHMS FOR THE SUM OF 2 NON-LINEAR OPERATORS
    LIONS, PL
    MERCIER, B
    [J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1979, 16 (06) : 964 - 979
  • [10] Partial differential variational inequalities involving nonlocal boundary conditions in Banach spaces
    Liu, Zhenhai
    Migorski, Stanislaw
    Zeng, Shengda
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2017, 263 (07) : 3989 - 4006
123