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.

Accepted:

DOI: 10.1051/cocv/2015053

Keywords: Quasi variational inequality, vector optimization, gap function, duality, saddle point

^{1}; Soleimani-damaneh, Majid

^{2, 3}

@article{COCV_2017__23_1_297_0, author = {Mirzaee, Hadi and Soleimani-damaneh, Majid}, 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://archive.numdam.org/articles/10.1051/cocv/2015053/} }

TY - JOUR AU - Mirzaee, Hadi AU - Soleimani-damaneh, Majid TI - Optimality, duality and gap function for quasi variational inequality problems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2017 SP - 297 EP - 308 VL - 23 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2015053/ DO - 10.1051/cocv/2015053 LA - en ID - COCV_2017__23_1_297_0 ER -

%0 Journal Article %A Mirzaee, Hadi %A Soleimani-damaneh, Majid %T Optimality, duality and gap function for quasi variational inequality problems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2017 %P 297-308 %V 23 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2015053/ %R 10.1051/cocv/2015053 %G en %F COCV_2017__23_1_297_0

Mirzaee, Hadi; Soleimani-damaneh, Majid. Optimality, duality and gap function for quasi variational inequality problems. ESAIM: Control, Optimisation and Calculus of Variations, Volume 23 (2017) no. 1, pp. 297-308. doi : 10.1051/cocv/2015053. http://archive.numdam.org/articles/10.1051/cocv/2015053/

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