Combinatorial Convexity in Hadamard Manifolds: Existence for Equilibrium Problems

Glaydston de Carvalho Bento (), João Xavier Cruz Neto () and Ítalo Dowell Lira Melo ()
Additional contact information
Glaydston de Carvalho Bento: Universidade Federal de Goiás
João Xavier Cruz Neto: Universidade Federal do Piauí
Ítalo Dowell Lira Melo: Universidade Federal do Piauí

Journal of Optimization Theory and Applications, 2022, vol. 195, issue 3, No 14, 1087-1105

Abstract: Abstract In this paper is introduced a proposal of resolvent for equilibrium problems in terms of the Busemann’s function. A advantage of this new proposal is that, in addition to be a natural extension of its counterpart in the linear setting introduced by Combettes and Hirstoaga (J Nonlinear Convex Anal 6(1): 117–136, 2005), 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. (J Convex Anal 24(2): 679–684, 2017 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 an associated Jensen-type inequality.

Keywords: Equilibrium problem; KKM’s lemma; Helly’s theorem; Hadamard manifold; 47N10; 47H05; 52A37 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-022-02112-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:195:y:2022:i:3:d:10.1007_s10957-022-02112-0

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-022-02112-0

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().