Optimization reformulations of the generalized Nash equilibrium problem using regularized indicator Nikaidô–Isoda function
In this paper, we extend the literature by adapting the Nikaidô–Isoda function as an indicator function termed as regularized indicator Nikaidô–Isoda function, and this is demonstrated to guarantee existence of a solution. Using this function, we present two constrained optimization reformulations o...
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| Published in | Journal of global optimization Vol. 57; no. 3; pp. 843 - 861 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Boston
Springer US
01.11.2013
Springer Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0925-5001 1573-2916 |
| DOI | 10.1007/s10898-012-9978-0 |
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| Abstract | In this paper, we extend the literature by adapting the Nikaidô–Isoda function as an indicator function termed as regularized indicator Nikaidô–Isoda function, and this is demonstrated to guarantee existence of a solution. Using this function, we present two constrained optimization reformulations of the generalized Nash equilibrium problem (GNEP for short). The first reformulation characterizes all the solutions of GNEP as global minima of the optimization problem. Later this approach is modified to obtain the second optimization reformulation whose global minima characterize the normalized Nash equilibria. Some numerical results are also included to illustrate the behaviour of the optimization reformulations. |
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| AbstractList | In this paper, we extend the literature by adapting the Nikaido-Isoda function as an indicator function termed as regularized indicator Nikaido-Isoda function, and this is demonstrated to guarantee existence of a solution. Using this function, we present two constrained optimization reformulations of the generalized Nash equilibrium problem (GNEP for short). The first reformulation characterizes all the solutions of GNEP as global minima of the optimization problem. Later this approach is modified to obtain the second optimization reformulation whose global minima characterize the normalized Nash equilibria. Some numerical results are also included to illustrate the behaviour of the optimization reformulations. Keywords Generalized Nash equilibrium problem * Regularized indicator Nikaido- Isoda function * Optimization reformulations * Normalized Nash equilibria * Quasi-variational inequality problem Mathematics Subject Classification (2000) 90C30 * 91A10 In this paper, we extend the literature by adapting the Nikaidô-Isoda function as an indicator function termed as regularized indicator Nikaidô-Isoda function, and this is demonstrated to guarantee existence of a solution. Using this function, we present two constrained optimization reformulations of the generalized Nash equilibrium problem (GNEP for short). The first reformulation characterizes all the solutions of GNEP as global minima of the optimization problem. Later this approach is modified to obtain the second optimization reformulation whose global minima characterize the normalized Nash equilibria. Some numerical results are also included to illustrate the behaviour of the optimization reformulations.[PUBLICATION ABSTRACT] In this paper, we extend the literature by adapting the Nikaidô–Isoda function as an indicator function termed as regularized indicator Nikaidô–Isoda function, and this is demonstrated to guarantee existence of a solution. Using this function, we present two constrained optimization reformulations of the generalized Nash equilibrium problem (GNEP for short). The first reformulation characterizes all the solutions of GNEP as global minima of the optimization problem. Later this approach is modified to obtain the second optimization reformulation whose global minima characterize the normalized Nash equilibria. Some numerical results are also included to illustrate the behaviour of the optimization reformulations. In this paper, we extend the literature by adapting the Nikaido-Isoda function as an indicator function termed as regularized indicator Nikaido-Isoda function, and this is demonstrated to guarantee existence of a solution. Using this function, we present two constrained optimization reformulations of the generalized Nash equilibrium problem (GNEP for short). The first reformulation characterizes all the solutions of GNEP as global minima of the optimization problem. Later this approach is modified to obtain the second optimization reformulation whose global minima characterize the normalized Nash equilibria. Some numerical results are also included to illustrate the behaviour of the optimization reformulations. |
| Audience | Academic |
| Author | Lalitha, C. S. Dhingra, Mansi |
| Author_xml | – sequence: 1 givenname: C. S. surname: Lalitha fullname: Lalitha, C. S. organization: Department of Mathematics, University of Delhi South Campus – sequence: 2 givenname: Mansi surname: Dhingra fullname: Dhingra, Mansi email: mansidhingra7@gmail.com organization: Department of Mathematics, University of Delhi |
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| CitedBy_id | crossref_primary_10_1590_0101_7438_2014_034_03_0521 crossref_primary_10_1016_j_ijepes_2021_106980 crossref_primary_10_1007_s40565_017_0359_z crossref_primary_10_1155_2020_1073412 |
| Cites_doi | 10.1109/9.293193 10.1080/10556780903448052 10.1007/BF01585696 10.1007/s10589-007-9145-6 10.1023/A:1021022522035 10.1287/opre.34.3.410 10.2140/pjm.1955.5.807 10.1002/cpa.3160200302 10.1287/moor.28.3.533.16395 10.1007/s10107-007-0156-y 10.1016/0377-2217(91)90325-P 10.1007/s10479-009-0653-x 10.1007/s10898-009-9420-4 10.1137/0312037 10.1109/TPWRS.2003.820692 10.1137/0312021 10.1023/A:1026050425030 10.1007/978-0-387-21738-3 |
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| Keywords | 91A10 Optimization reformulations 90C30 Regularized indicator Nikaidô–Isoda function Normalized Nash equilibria Quasi-variational inequality problem Generalized Nash equilibrium problem |
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| Title | Optimization reformulations of the generalized Nash equilibrium problem using regularized indicator Nikaidô–Isoda function |
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