Elements of Convex Geometry in Hadamard Manifolds with Application to Equilibrium Problems
Abstract
In this paper, is introduced a new proposal of resolvent for equilibrium problems in terms of the Busemann's function. A great advantage of this new proposal is that, in addition to be a natural extension of the proposal in the linear setting by Combettes and Hirstoaga in [20], the new term that performs regularization is a convex function in general Hadamard manifolds, being a first step to fully answer to the problem posed by Cruz Neto et al. in [21, Section 5]. During our study, some elements of convex analysis are explored in the context of Hadamard manifolds, which are interesting on their own. In particular, we introduce a new definition of convex combination (now commutative) of any finite collection of points and present the realization of an associated Jensen-type inequality.
Keywords
Cite
@article{arxiv.2107.02223,
title = {Elements of Convex Geometry in Hadamard Manifolds with Application to Equilibrium Problems},
author = {G. C. Bento and J. X. Cruz Neto and I. D. L. Melo},
journal= {arXiv preprint arXiv:2107.02223},
year = {2021}
}
Comments
22 pages