Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/16871
Title: Weak sharp minima for set-valued vector variational inequalities with an application
Authors: Li, J
Huang, NJ
Yang, XQ 
Keywords: Gap function
Set-valued weak (res., strong) vector variational inequality
Strong convexity
Strong pseudomonotonicity
Weak sharp minimum
Issue Date: 2010
Publisher: Elsevier
Source: European journal of operational research, 2010, v. 205, no. 2, p. 262-272 How to cite?
Journal: European journal of operational research 
Abstract: In this paper, the notion of weak sharp minima is employed to the investigation of set-valued vector variational inequalities. The gap function φT for set-valued strong vector variational inequalities (for short, SVVI) is proved to be less than the gap function φ{symbol}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 sqrt(min1 ≤ i ≤ n pTi) and for gap functions sqrt(φT) and sqrt(φ{symbol}T) 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 sqrt(min1 ≤ i ≤ n p∇ gi) when each component gi of objective function is strongly convex.
URI: http://hdl.handle.net/10397/16871
ISSN: 0377-2217
EISSN: 1872-6860
DOI: 10.1016/j.ejor.2010.01.004
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