A parallel hybrid accelerated extragradient algorithm for pseudomonotone equilibrium, fixed point, and split null point problems

Yasir Arfat,Attapol Kaewkhao,Poom Kumam,Parinya Sa Ngiamsunthorn,Muhammad Aqeel Ahmad Khan

doi:10.1186/s13662-021-03518-2

Abstract

This paper provides iterative construction of a common solution associated with the classes of equilibrium problems (EP) and split convex feasibility problems. In particular, we are interested in the EP defined with respect to the pseudomonotone bifunction, the fixed point problem (FPP) for a finite family of -demicontractive operators, and the split null point problem. From the numerical standpoint, combining various classical iterative algorithms to study two or more abstract problems is a fascinating field of research. We, therefore, propose an iterative algorithm that combines the parallel hybrid extragradient algorithm with the inertial extrapolation technique. The analysis of the proposed algorithm comprises theoretical results concerning strong convergence under a suitable set of constraints and numerical results.

Highlights

1 Introduction The class of convex feasibility problems (CFP) has been widely studied in the current literature as it encompasses a variety of problems arising in mathematical and physical sciences
Numerous iterative algorithms have been studied to obtain an approximate solution for the CFP in Hilbert spaces
The class of projection algorithms is prominent among various iterative algorithms to solve the CFP

Summary

Introduction

The class of convex feasibility problems (CFP) has been widely studied in the current literature as it encompasses a variety of problems arising in mathematical and physical sciences. In 1994, Blum and Oettli [7] proposed, in a mathematical formulation, an EP with respect to a (monotone) bifunction g defined on a nonempty subset C of a real Hilbert space H1 that aims to find a point x ∈ C such that g(x, y) ≥ 0 for all y ∈ C. Let T : C → C be an operator defined on a nonempty subset C of a real Hilbert space H1, T is known as nonexpansive if Tx – Ty ≤ x – y for all x, y ∈ C.

Results

Conclusion