Work

An Approximation Algorithm for the Combination of G-Variational Inequalities and Fixed Point Problems

Year: 2024

Type: article

Abstract: In this paper, we introduce a modified form of the G-variational inequality problem, called the combination of G-variational inequalities problem, within a Hilbert space structured by graphs. Furthermore, we develop an iterative scheme to find a common element between the set of fixed points of a G-nonexpansive mapping and the solution set of the proposed G-variational inequality problem. Under appropriate assumptions, we establish a strong convergence theorem within the framework of a Hilbert space endowed with graphs. Additionally, we present the concept of the G-minimization problem, which diverges from the conventional minimization problem. Applying our main results, we demonstrate a strong convergence theorem for the G-minimization problem. Finally, we provide illustrative examples to validate and support our theoretical findings.

Source: Mathematics

DOI: 10.3390/math13010122

Authors: Araya Kheawborisut, Atid Kangtunyakarn

Institution: King Mongkut's Institute of Technology Ladkrabang

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,955

Funder: King Mongkut's Institute of Technology Ladkrabang