![](/images/graphics-bg.png)
A New Algorithm to Solve the Generalized Nash Equilibrium Problem
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-10-02
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
We try a new algorithm to solve the generalized Nash equilibrium problem (GNEP) in the paper.
First, the GNEP is turned into the nonlinear complementarity problem by using the Karush–Kuhn–Tucker (KKT) condition.
Then, the nonlinear complementarity problem is converted into the nonlinear equation problem by using the complementarity function method.
For the nonlinear equation equilibrium problem, we design a coevolutionary immune quantum particle swarm optimization algorithm (CIQPSO) by involving the immune memory function and the antibody density inhibition mechanism into the quantum particle swarm optimization algorithm.
Therefore, this algorithm has not only the properties of the immune particle swarm optimization algorithm, but also improves the abilities of iterative optimization and convergence speed.
With the probability density selection and quantum uncertainty principle, the convergence of the CIQPSO algorithm is analyzed.
Finally, some numerical experiment results indicate that the CIQPSO algorithm is superior to the immune particle swarm algorithm, the Newton method for normalized equilibrium, or the quasivariational inequalities penalty method.
Furthermore, this algorithm also has faster convergence and better off-line performance.
American Psychological Association (APA)
Liu, Luping& Jia, Wensheng. 2020. A New Algorithm to Solve the Generalized Nash Equilibrium Problem. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-9.
https://search.emarefa.net/detail/BIM-1193038
Modern Language Association (MLA)
Liu, Luping& Jia, Wensheng. A New Algorithm to Solve the Generalized Nash Equilibrium Problem. Mathematical Problems in Engineering No. 2020 (2020), pp.1-9.
https://search.emarefa.net/detail/BIM-1193038
American Medical Association (AMA)
Liu, Luping& Jia, Wensheng. A New Algorithm to Solve the Generalized Nash Equilibrium Problem. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-9.
https://search.emarefa.net/detail/BIM-1193038
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1193038