The convergence rate of a golden ratio algorithm for equilibrium problems

TL;DR

This paper proves the R-linear convergence rate of a golden ratio algorithm for equilibrium problems in Hilbert spaces and demonstrates its effectiveness through numerical experiments.

Contribution

It establishes the R-linear convergence rate of a new golden ratio algorithm for equilibrium problems, with empirical validation.

Findings

The algorithm converges at an R-linear rate.

Numerical experiments confirm the algorithm's efficiency.

Comparison shows advantages over existing methods.

Abstract

In this paper, we establish the $R$-linear rate of convergence of a golden ratio algorithm for solving an equilibrium problem in a Hilbert space. Several experiments are performed to show the numerical behavior of the algorithm and also to compare with others.