Strong convergence inertial projection algorithm with self-adaptive step size rule for pseudomonotone variational inequalities in Hilbert spaces-Reference-Cited by-同舟云学术

Strong convergence inertial projection algorithm with self-adaptive step size rule for pseudomonotone variational inequalities in Hilbert spaces

Published:2021-01-01 Issue:1 Volume:54 Page:110-128
ISSN:2391-4661
Container-title:Demonstratio Mathematica
language:en
Short-container-title:

Author:

Wairojjana Nopparat¹,Pakkaranang Nuttapol²,Pholasa Nattawut³

Affiliation:

1. Applied Mathematics Program, Faculty of Science and Technology, Valaya Alongkorn Rajabhat University under the Royal Patronage (VRU), 1 Moo 20 Phaholyothin Road, Klong Neung , Klong Luang , Pathumthani 13180 , Thailand

2. Department of Mathematics, Faculty of Science and Technology, Phetchabun Rajabhat University , Phetchabun 67000 , Thailand

3. School of Science, University of Phayao , Phayao 56000 , Thailand

Abstract

Abstract In this paper, we introduce a new algorithm for solving pseudomonotone variational inequalities with a Lipschitz-type condition in a real Hilbert space. The algorithm is constructed around two algorithms: the subgradient extragradient algorithm and the inertial algorithm. The proposed algorithm uses a new step size rule based on local operator information rather than its Lipschitz constant or any other line search scheme and functions without any knowledge of the Lipschitz constant of an operator. The strong convergence of the algorithm is provided. To determine the computational performance of our algorithm, some numerical results are presented.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/dema-2021-0011/pdf

Reference37 articles.

1. G. Stampacchia , Formes bilinéaires coercitives sur les ensembles convexes, Académie des Sciences de Paris 258 (1964), 4413–4416.

2. I. V. Konnov , On systems of variational inequalities, Izv. Vyssh. Uchebn. Zaved. Mat. 41 (1997), 77–86.

3. G. Kassay , J. Kolumbán , and Z. Páles , On Nash stationary points, Publ. Math. Debrecen 54 (1999), no. 3–4, 267–279.

4. G. Kassay , J. Kolumbán , and Z. Páles , Factorization of minty and stampacchia variational inequality systems, European J. Oper. Res. 143 (2002), no. 2, 377–389.

5. D. Kinderlehrer and G. Stampacchia , An Introduction to Variational Inequalities and Their Applications , Classics in Applied Mathematics , vol. 31, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2000.

Cited by 7 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Efficiency of a New Iterative Algorithm Using Fixed-Point Approach in the Settings of Uniformly Convex Banach Spaces;Axioms;2024-07-26

2. A solution of a fractional differential equation via novel fixed-point approaches in Banach spaces;AIMS Mathematics;2023

3. On Strengthened Extragradient Methods Non-Convex Combination with Adaptive Step Sizes Rule for Equilibrium Problems;Symmetry;2022-05-19

4. A Self-Adaptive Extragradient Algorithm for Solving Quasimonotone Variational Inequalities;Journal of Function Spaces;2022-03-31

5. A strong convergence algorithm for solving pseudomonotone variational inequalities with a single projection;The Journal of Analysis;2022-01-25