A HYBRID STEEPEST DESCENT METHOD FOR BILEVEL VARIATIONAL INEQUALITY PROBLEMS WITH THE FIXED POINT SET

被引：0

作者：

Ram, Tirth ^{[1
]}

Iqbal, Mohd ^{[1
]}

Bhagat, Zeenat ^{[1
]}

机构：

[1] Univ Jammu, Dept Math, Jammu 180006, India

来源：

JOURNAL OF INEQUALITIES AND SPECIAL FUNCTIONS | 2024年 / 15卷 / 03期

关键词：

fixed point; bilevel variational inequality; Hilbert space; descent method; Lipschitz continuous; nonexpansive mapping; STRONG-CONVERGENCE; PROJECTION; ALGORITHM; STEP;

D O I：

10.54379/JIASF-2024-3-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we present a new hybrid steepest decent algorithm to solve the bilevel variational inequality problems, where the feasible set is the intersection of a variational inequality problem and the fixed point set of a nonexpansive mapping in a real Hilbert space. An iterative algorithm is introduced by using the hybrid steepest descent method and fixed-point formulation techniques. The strong convergence of the iterative sequences generated by the algorithm is shown under some suitable assumptions. In addition, the efficiency of our suggested algorithm is established by a numerical example.

引用

页码：1 / 12

页数：12

共 50 条

[1] Hybrid steepest descent method for variational inequality problem over the fixed point set of certain quasi-nonexpansive mappings
Yamada, I
Ogura, N
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2004, 25 (7-8) : 619 - 655
[2] A Viscosity Hybrid Steepest Descent Method for Equilibrium Problems, Variational Inequality Problems, and Fixed Point Problems of Infinite Family of Strictly Pseudocontractive Mappings and Nonexpansive Semigroup
Che, Haitao
Pan, Xintian
ABSTRACT AND APPLIED ANALYSIS, 2013,
[3] The hybrid steepest descent method for solving variational inequality over triple hierarchical problems
Nopparat Wairojjana
Thanyarat Jitpeera
Poom Kumam
Journal of Inequalities and Applications, 2012
[4] The hybrid steepest descent method for solving variational inequality over triple hierarchical problems
Wairojjana, Nopparat
Jitpeera, Thanyarat
Kumam, Poom
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2012,
[5] Inertial Method for Bilevel Variational Inequality Problems with Fixed Point and Minimizer Point Constraints
Yimer, Seifu Endris
Kumam, Poom
Gebrie, Anteneh Getachew
Wangkeeree, Rabian
MATHEMATICS, 2019, 7 (09)
[6] Extension of the hybrid steepest descent method to a class of variational inequalities and fixed point problems with nonself-mappings
Mainge, Paul-Emile
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2008, 29 (7-8) : 820 - 834
[7] The Hybrid Steepest Descent Method for Addressing Fixed Point Problems and System of Equilibrium Problems
Jaiboon, Chaichana.
THAI JOURNAL OF MATHEMATICS, 2010, 8 (02): : 275 - 292
[8] An inertial method for solving bilevel variational inequality problems with fixed point constraints
Yirga Abebe Belay
Habtu Zegeye
Oganeditse A. Boikanyo
Dintle Kagiso
Hagos Hailu Gidey
ANNALI DELL'UNIVERSITA' DI FERRARA, 2025, 71 (1)
[9] A New Hybrid Method for Variational Inequality and Fixed Point Problems
Thuy N.T.T.
Vietnam Journal of Mathematics, 2013, 41 (3) : 353 - 366
[10] The hybrid steepest descent method for solutions of equilibrium problems and other problems in fixed point theory
Micha O Osilike
Eric U Ofoedu
Felix U Attah
Fixed Point Theory and Applications, 2014

← 1 2 3 4 5 →