Geodesic
Optimality, duality and gap function for quasi variational inequality problems
Mirzaee, Hadi1 ; Soleimani-damaneh, Majid2, 3
1 Faculty of Mathematical and Computer Science, Kharazmi University, 50 Taleghani Avenue, 15618 Tehran, Iran
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
ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 1, pp. 297-308

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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.

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Accepté le :
DOI : 10.1051/cocv/2015053
Classification : 49J27, 49J40, 49J52
Keywords: Quasi variational inequality, vector optimization, gap function, duality, saddle point

Mirzaee, Hadi 1 ; Soleimani-damaneh, Majid 2, 3

1 Faculty of Mathematical and Computer Science, Kharazmi University, 50 Taleghani Avenue, 15618 Tehran, Iran
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 
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     title = {Optimality, duality and gap function for quasi variational inequality problems},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {297--308},
     publisher = {EDP-Sciences},
     volume = {23},
     number = {1},
     year = {2017},
     doi = {10.1051/cocv/2015053},
     mrnumber = {3601025},
     zbl = {1365.49013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2015053/}
}
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Mirzaee, Hadi; Soleimani-damaneh, Majid. Optimality, duality and gap function for quasi variational inequality problems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 1, pp. 297-308. doi: 10.1051/cocv/2015053

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