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arXiv · 2506.22391

Regularized Extragradient Methods for Solving Equilibrium Problems on Hadamard Manifolds

Shikher Sharmaa·Pankaj Gautam·Simeon Reich
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Abstract

Employing two distinct types of regularization terms, we propose two regularized extragradient methods for solving equilibrium problems on Hadamard manifolds. The sequences generated by these extragradient algorithms converge to a solution of the equilibrium problem without requiring the Lipschitz continuity of the bifunction or imposing additional conditions on the parameters. We establish convergence results for both algorithms under a monotonicity condition and derive global error bounds along with $R$-linear convergence rates in cases where the bifunction is strongly pseudomonotone. Finally, we present numerical experiments to demonstrate the effectiveness of our methods.

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Shikher Sharmaa, Pankaj Gautam, Simeon Reich. 2025-06-27. Regularized Extragradient Methods for Solving Equilibrium Problems on Hadamard Manifolds. https://arxiv.org/abs/2506.22391

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