Weak sharp minima for set-valued vector variational inequalities with an application

J. Li, N.J. Huang and X.Q. Yang

European Journal of Operational Research, 2010, vol. 205, issue 2, 262-272

Abstract: In this paper, the notion of weak sharp minima is employed to the investigation of set-valued vector variational inequalities. The gap function [phi]T for set-valued strong vector variational inequalities (for short, SVVI) is proved to be less than the gap function [phi]T for set-valued weak vector variational inequalities (for short, WVVI) under certain conditions, which implies that the solution set of SVVI is equivalent to the solution set of WVVI. Moreover, it is shown that weak sharp minima for the solution sets of SVVI and WVVI hold for and for gap functions and under the assumption of strong pseudomonotonicity, where pTi is a gap function for i-th component of SVVI and WVVI. As an application, the weak Pareto solution set of vector optimization problems (for short, VOP) is proved to be weak sharp minimum for when each component gi of objective function is strongly convex.

Keywords: Set-valued weak (res.; strong) vector variational inequality Gap function Weak sharp minimum Strong pseudomonotonicity Strong convexity (search for similar items in EconPapers)
Date: 2010
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0377-2217(10)00012-3
Full text for ScienceDirect subscribers only

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:eee:ejores:v:205:y:2010:i:2:p:262-272

Access Statistics for this article

European Journal of Operational Research is currently edited by Roman Slowinski, Jesus Artalejo, Jean-Charles. Billaut, Robert Dyson and Lorenzo Peccati

More articles in European Journal of Operational Research from Elsevier
Bibliographic data for series maintained by Catherine Liu ().