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.