Nonsmooth Vector Optimization Problems and Minty Vector Variational Inequalities

Q. H. Ansari () and G. M. Lee ()
Additional contact information
Q. H. Ansari: Aligarh Muslim University
G. M. Lee: Pukyong National University

Journal of Optimization Theory and Applications, 2010, vol. 145, issue 1, No 1, 16 pages

Abstract: Abstract The vector optimization problem may have a nonsmooth objective function. Therefore, we introduce the Minty vector variational inequality (Minty VVI) and the Stampacchia vector variational inequality (Stampacchia VVI) defined by means of upper Dini derivative. By using the Minty VVI, we provide a necessary and sufficient condition for a vector minimal point (v.m.p.) of a vector optimization problem for pseudoconvex functions involving Dini derivatives. We establish the relationship between the Minty VVI and the Stampacchia VVI under upper sign continuity. Some relationships among v.m.p., weak v.m.p., solutions of the Stampacchia VVI and solutions of the Minty VVI are discussed. We present also an existence result for the solutions of the weak Minty VVI and the weak Stampacchia VVI.

Keywords: Minty vector variational inequalities; Stampacchia vector variational inequalities; Vector optimization problems; Vector minimal points; Weak vector minimal points; Dini derivative; Pseudoconvex functions; Upper sign continuity (search for similar items in EconPapers)
Date: 2010
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (8)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-009-9638-9 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:joptap:v:145:y:2010:i:1:d:10.1007_s10957-009-9638-9

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

DOI: 10.1007/s10957-009-9638-9

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 ().