NDLI: On the Existence of Projected Solutions of Quasi-Variational Inequalities and Generalized Nash Equilibrium Problems

Content Provider	Springer Nature Link
Author	Sultana, Asrifa Aussel, Didier Vetrivel, Vellaichamy
Copyright Year	2016
Abstract	A quasi-variational inequality is a variational inequality, in which the constraint set is depending on the variable. However, as shown by a motivating example in electricity market, the constraint map may not be a self-map, and then, there is usually no solution. Thus, we define the concept of projected solution and, based on a fixed point theorem, we establish some results on existence of projected solution for quasi-variational inequality problem in a finite-dimensional space where the constraint map is not necessarily self-map. As an application of our results, we obtain an existence theorem for quasi-optimization problems. Finally, we introduce the concept of projected Nash equilibrium and study the existence of such equilibrium for noncooperative games as another application.
Ending Page	837
Page Count	20
Starting Page	818
File Format	PDF
ISSN	00223239
e-ISSN	15732878
Journal	Journal of Optimization Theory and Applications
Issue Number	3
Volume Number	170
Language	English
Publisher	Springer US
Publisher Date	2016-05-23
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Engineering Calculus of Variations and Optimal Control; Optimization Nonconvex programming, global optimization Quasi-variational inequality Network models, deterministic Theory of Computation Generalized Nash equilibrium Applications of Mathematics Operation Research/Decision Theory Variational methods including variational inequalities Non-self map Optimization
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Control and Optimization Management Science and Operations Research

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