Volume 23, Number 1, January-March 2017
|Page(s)||297 - 308|
|Published online||13 December 2016|
Optimality, duality and gap function for quasi variational inequality problems
1 Faculty of Mathematical and Computer
Science, Kharazmi University, 50
Taleghani Avenue, 15618
2 School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran
3 School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran, Iran
Revised: 5 July 2015
Accepted: 14 December 2015
This paper deals with the Quasi Variational Inequality (QVI) problem on Banach spaces. Necessary and sufficient conditions for the solutions of QVI are given, using the subdifferential of distance function and the normal cone. A dual problem corresponding to QVI is constructed and strong duality is established. The solutions of dual problem are characterized according to the saddle points of the Lagrangian map. A gap function for dual of QVI is presented and its properties are established. Moreover, some applied examples are addressed.
Mathematics Subject Classification: 49J27 / 49J40 / 49J52
Key words: Quasi variational inequality / vector optimization / gap function / duality / saddle point
© EDP Sciences, SMAI 2016
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