Work

An Adapted Proximal Point Algorithm Utilizing the Golden Ratio Technique for Solving Equilibrium Problems in Banach Spaces

Year: 2024

Type: article

Abstract: This paper explores the iterative approximation of solutions to equilibrium problems and proposes a simple proximal point method for addressing them. We incorporate the golden ratio technique as an extrapolation method, resulting in a two-step iterative process. This method is self-adaptive and does not require any Lipschitz-type conditions for implementation. We present and prove a weak convergence theorem along with a sublinear convergence rate for our method. The results extend some previously published findings from Hilbert spaces to 2-uniformly convex Banach spaces. To demonstrate the effectiveness of the method, we provide several numerical illustrations and compare the results with those from other methods available in the literature.

Source: Mathematics

DOI: 10.3390/math12233773

Authors: Hammed Anuoluwapo Abass, Olawale Kazeem Oyewole, Seithuti Philemon Moshokoa, Abubakar Adamu

Institutions: Sefako Makgatho Health Sciences University, Tshwane University of Technology, African Institute of Science and Technology, Near East University

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

OpenAlex ID: W4404931499

FWCI: 0.39

Cites: 34

Cited by: 2

Related to: 10