Linear conditioning, weak sharpness and finite convergence for equilibrium problems

Luong Nguyen (), Qamrul Hasan Ansari () and Xiaolong Qin ()
Additional contact information
Luong Nguyen: Hong Duc University
Qamrul Hasan Ansari: Aligarh Muslim University
Xiaolong Qin: Hangzhou Normal University

Journal of Global Optimization, 2020, vol. 77, issue 2, No 10, 405-424

Abstract: Abstract The present paper first provides sufficient conditions and characterizations for linearly conditioned bifunction associated with an equilibrium problem. It then introduces the notion of weak sharp solution for equilibrium problems which is analogous to the linear conditioning notion. This new notion generalizes and unifies the notion of weak sharp minima for optimization problems as well as the notion of weak sharp solutions for variational inequality problems. Some sufficient conditions and characterizations of weak sharpness are also presented. Finally, we study the finite convergence property of sequences generated by some algorithms for solving equilibrium problems under linear conditioning and weak shapness assumptions. An upper bound of the number of iterations by which the sequence generated by proximal point algorithm converges to a solution of equilibrium problems is also given.

Keywords: Equilibrium problems; Linear conditioning; Weak sharpness; Finite convergence; Inexact proximal point algorithm.; 49J40; 47J20; 90C33; 65K10; 65K15 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1007/s10898-019-00869-9 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:jglopt:v:77:y:2020:i:2:d:10.1007_s10898-019-00869-9

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/10898

DOI: 10.1007/s10898-019-00869-9

Access Statistics for this article

Journal of Global Optimization is currently edited by Sergiy Butenko

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