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

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