An explicit extragradient algorithm for equilibrium problems on Hadamard manifolds

TL;DR

This paper introduces a new extragradient algorithm with variable stepsize for solving equilibrium problems on Hadamard manifolds, demonstrating convergence and efficiency improvements over existing methods.

Contribution

It proposes a novel extragradient algorithm tailored for equilibrium problems on Hadamard manifolds, including convergence analysis and numerical validation.

Findings

The algorithm converges under mild assumptions.

It achieves an R-linear rate of convergence for strongly pseudomonotone bifunctions.

Numerical experiments illustrate the algorithm's effective behavior.

Abstract

In this paper, we investigate a new extragradient algorithm for solving pseudomonotone equilibrium problems on Hadamard manifolds. The algorithm uses a variable stepsize which is updated at each iteration and based on some previous iterates. The convergence analysis of the proposed algorithm is discussed under mild assumptions. In the case where the equilibrium bifunction is strongly pseudomonotone, the $R$-linear rate of convergence of the new algorithm is formulated. A fundamental experiment is provided to illustrate the numerical behavior of the algorithm. The results presented in this paper generalize some corresponding known results.