A Bregman Regularized Proximal Point Method for Solving Equilibrium Problems on Hadamard Manifolds

A Bregman Regularized Proximal Point Method for Solving Equilibrium Problems on Hadamard Manifolds

A Bregman Regularized Proximal Point Method for Solving Equilibrium Problems on Hadamard Manifolds

Sunday, July 26, 2026
  • Lecturer: Shikher Sharma (Technion)
  • Organizer: Simeon Reich
  • Location: Amado 814
Abstract:
Abstract We present a Bregman regularized proximal point algorithm for solving monotone equilibrium problems on Hadamard manifolds. It has been shown that the regularization term induced by a Bregman function is, in general, nonconvex on Hadamard manifolds unless the curvature is zero. Nevertheless, we prove that the proposed Bregman regularization scheme does converge to a solution of the equilibrium problem on Hadamard manifolds in the presence of a strong assumption on the convexity of a certain set formed by the regularization term. Moreover, we employ a coercivity condition on the Bregman function which is weaker than those typically assumed in the existing literature on Bregman regularization. Numerical experiments on illustrative examples demonstrate the practical effectiveness of our proposed method. This is joint work with Simeon Reich (Technion–Israel Institute of Technology). Keywords. Bregman distance; Equilibrium problems; Hadamard manifolds; Proximal methods.
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