On the Relationship Between the Kurdyka–Łojasiewicz Property and Error Bounds on Hadamard Manifolds

João Xavier Cruz Neto (), Ítalo Dowell Lira Melo (), Paulo Alexandre Sousa () and João Carlos Oliveira Souza ()
Additional contact information
João Xavier Cruz Neto: Federal University of Piauí
Ítalo Dowell Lira Melo: Federal University of Piauí
Paulo Alexandre Sousa: Federal University of Piauí
João Carlos Oliveira Souza: Federal University of Piauí

Journal of Optimization Theory and Applications, 2024, vol. 200, issue 3, No 14, 1255-1285

Abstract: Abstract This paper studies the interplay between the concepts of error bounds and the Kurdyka–Łojasiewicz (KL) inequality on Hadamard manifolds. To this end, we extend some properties and existence results of a solution for differential inclusions on Hadamard manifolds. As a second contribution, we show how the KL inequality can be used to obtain the convergence of the gradient method for solving convex feasibility problems on Hadamard manifolds. The convergence results of the alternating projection method are also established for cyclic and random projections on Hadamard manifolds and, more generally, CAT(0) spaces.

Keywords: Differential inclusion; Kurdyka–Łojasiewicz inequality; Error bounds; Convex feasibility problem; Hadamard manifolds; CAT(0) spaces; 65K10; 90C30; 49M99; 65J05 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-024-02386-6 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:200:y:2024:i:3:d:10.1007_s10957-024-02386-6

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

DOI: 10.1007/s10957-024-02386-6

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 ().