Levitin–Polyak Well-Posedness by Perturbations for the Split Hemivariational Inequality Problem on Hadamard Manifolds

Vo Minh Tam (), Nguyen Hung (), Zhenhai Liu () and Jen Chih Yao ()
Additional contact information
Vo Minh Tam: Dong Thap University
Nguyen Hung: Posts and Telecommunications Institute of Technology
Zhenhai Liu: Guangxi Minzu University
Jen Chih Yao: China Medical University

Journal of Optimization Theory and Applications, 2022, vol. 195, issue 2, No 14, 684-706

Abstract: Abstract The purpose of this paper is to establish some new results on the Levitin–Polyak well-posedness to a class of split hemivariational inequality problems on Hadamard manifolds. We first consider a new class of split hemivariational inequality problems (for short, SHIP) on Hadamard manifolds and introduce the regularized gap functions for these problems. Then, we study the notion of Levitin–Polyak well-posedness by perturbations to SHIP and show the equivalence between the Levitin–Polyak well-posedness by perturbations and the existence of solutions for SHIP under suitable conditions. Furthermore, based on the regularized gap functions for the perturbed SHIP, we establish the criterion for the Levitin–Polyak well-posedness by perturbations for SHIP via the split optimization problems on Hadamard manifolds. Our main results presented in paper are new even in the special case of hemivariational inequality problems.

Keywords: Split hemivariational inequality problem; Regularized gap function; Levitin–Polyak well-posedness; Hadamard manifold; 47J20; 49J40; 49K40 (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/s10957-022-02111-1 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:2:d:10.1007_s10957-022-02111-1

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

DOI: 10.1007/s10957-022-02111-1

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 ().