On the Existence of Projected Solutions of Quasi-Variational Inequalities and Generalized Nash Equilibrium Problems
| Autor: | Asrifa Sultana, Didier Aussel, V. Vetrivel |
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| Rok vydání: | 2016 |
| Předmět: |
021103 operations research
Control and Optimization Applied Mathematics 0211 other engineering and technologies Fixed-point theorem Existence theorem 010103 numerical & computational mathematics 02 engineering and technology Management Science and Operations Research 01 natural sciences Constraint (information theory) symbols.namesake Nash equilibrium Variational inequality Theory of computation symbols 0101 mathematics Epsilon-equilibrium Solution concept Mathematical economics Mathematics |
| Zdroj: | Journal of Optimization Theory and Applications. 170:818-837 |
| ISSN: | 1573-2878 0022-3239 |
| DOI: | 10.1007/s10957-016-0951-9 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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