On the computation of Nash and Pareto equilibria for some bi-objective control problems for the wave equation

This paper deals with the numerical implementation of a systematic method for solving bi-objective optimal control problems for wave equations. More precisely, we look for Nash and Pareto equilibria which respectively correspond to appropriate noncooperative and cooperative strategies in multi-objec...

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Bibliographic Details
Published in:Advances in computational mathematics 2020-10, Vol.46 (5), Article 73
Main Authors: de Carvalho, Pitágoras Pinheiro, Fernández-Cara, Enrique, Ferrel, Juan Bautista Límaco
Format: Article
Language:English
Subjects:
Algorithms
Computational mathematics
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Control methods
Finite difference method
Mathematical analysis
Mathematical and Computational Biology
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Numerical methods
Optimal control
Visualization
Wave equations
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Summary:This paper deals with the numerical implementation of a systematic method for solving bi-objective optimal control problems for wave equations. More precisely, we look for Nash and Pareto equilibria which respectively correspond to appropriate noncooperative and cooperative strategies in multi-objective optimal control. The numerical methods described here consist of a combination of the following: finite element techniques for space approximation; finite difference schemes for time discretization; gradient algorithms for the solution of the discrete control problems. The efficiency of the computational methods is illustrated by the results of some numerical experiments.
ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-020-09812-z