Vector variational inequalities and their relations with vector optimization

Authors

  • Surjeet Kaur Suneja Department of Mathematics, Miranda House, University of Delhi, Delhi-110007, India
  • Bhawna Kohli

DOI:

https://doi.org/10.11121/ijocta.01.2014.00160

Keywords:

Generalized nonsmooth cone convexity, generalized cone monotonicity, vector optimization problem, vector variational inequality problem.

Abstract

In this paper, K- quasiconvex, K- pseudoconvex and other related functions have been introduced in terms of their Clarke subdifferentials, where   is an arbitrary closed convex, pointed cone with nonempty interior. The (strict, weakly) -pseudomonotonicity, (strict) Knaturally quasimonotonicity and K- quasimonotonicity of Clarke subdifferential maps have also been defined. Further, we introduce Minty weak (MVVIP) and Stampacchia weak (SVVIP) vector variational inequalities over arbitrary cones. Under regularity assumption, we have proved that a weak minimum solution of vector optimization problem (VOP) is a solution of (SVVIP) and under the condition of K- pseudoconvexity we have obtained the converse for MVVIP (SVVIP). In the end we study the interrelations between these with the help of strict K-naturally quasimonotonicity of Clarke subdifferential map.

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Author Biographies

Surjeet Kaur Suneja, Department of Mathematics, Miranda House, University of Delhi, Delhi-110007, India

Prof, Department of Mathematics, University of Delhi, Delhi-110007, India

Bhawna Kohli

Assit. Prof., Department of Mathematics, University of Delhi, Delhi-110007, India

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Published

2013-12-10

How to Cite

Suneja, S. K., & Kohli, B. (2013). Vector variational inequalities and their relations with vector optimization. An International Journal of Optimization and Control: Theories &Amp; Applications (IJOCTA), 4(1), 35–44. https://doi.org/10.11121/ijocta.01.2014.00160

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Section

Applied Mathematics & Control