Vector variational inequalities involving vector maximal points

Authors:
M. H. Kim;S. H. Kum;G. M. Lee
Affiliations:
PhD Student, Department of Applied Mathematics, Pukyong National University, Pusan, Korea;Associate Professor, Department of Mathematics Education, Chungbuk National University, Cheongju, Korea;Professor, Department of Applied Mathematics, Pukyong National University, Pusan, Korea
Venue:
Journal of Optimization Theory and Applications
Year:
2002

Citing 4
Cited 1

Existence of solutions for a vector variational inequality: an extension of the Hartmann-Stampacchia theorem

Journal of Optimization Theory and Applications
Generalized convex functions and vector variational inequalities

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Vector variational inequality as a tool for studying vector optimization problems

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On implicit vector variational inequalities

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References on Vector Variational Inequalities

Journal of Global Optimization

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Abstract

This paper considers the existence of solutions and the equivalence of four kinds of vector variational inequalities (WI). More precisely, a sufficient condition is provided under which the solution sets of these VVIs are nonempty and equal. An example is given, showing that such a sufficient condition is essential to ensure the results. Actually, the main theorems in this paper can be regarded as a suitable correction and a refinement of recent results due to Chang et al. (Ref.1).