Variational Inequalities Characterizing Weak Minimality in Set Optimization

Giovanni P. Crespi (), Matteo Rocca () and Carola Schrage ()
Additional contact information
Giovanni P. Crespi: Loc. Grand Chemin 73-75
Matteo Rocca: Università degli Studi dell’Insubria
Carola Schrage: Loc. Grand Chemin 73-75

Journal of Optimization Theory and Applications, 2015, vol. 166, issue 3, No 6, 804-824

Abstract: Abstract We introduce the notion of weak minimizer in set optimization. Necessary and sufficient conditions in terms of scalarized variational inequalities of Stampacchia and Minty type, respectively, are proved. As an application, we obtain necessary and sufficient optimality conditions for weak efficiency of vector optimization in infinite-dimensional spaces. A Minty variational principle in this framework is proved as a corollary of our main result.

Keywords: Set optimization; Weak efficiency; Variational inequalities; Scalarization; 49J40; 49J53; 58C06; 58E30 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-014-0679-3 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:166:y:2015:i:3:d:10.1007_s10957-014-0679-3

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

DOI: 10.1007/s10957-014-0679-3

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 ().