Numerical methods for Nash equilibria in multiobjective control of partial differential equations
| dc.book.title | Analysis and optimization of differential systems : IFIP TC7-WG7.2 International Working Conference on Analysis and Optimization of Differential Systems, September 10-14, 2002, Constanta, Romania | |
| dc.contributor.author | Ramos Del Olmo, Ángel Manuel | |
| dc.contributor.editor | Barbu, Viorel | |
| dc.date.accessioned | 2023-06-20T21:03:58Z | |
| dc.date.available | 2023-06-20T21:03:58Z | |
| dc.date.issued | 2003 | |
| dc.description | Incluye colaboración de Luis Alberto Fernández Fernández y Cecilia Pola Méndez. | |
| dc.description.abstract | This paper is concerned with the numerical solution of multiobjective control problems associated with linear (resp., nonlinear) partial differential equations. More precisely, for such problems, we look for Nash equilibria, which are solutions to noncooperative games. First, we study the continuous case. Then, to compute the solution of the problem, we combine finite-difference methods for the time discretization, finite-element methods for the space discretization, and conjugate gradient algorithms (resp., a suitable algorithm) for the iterative solution of the discrete control problems. Finally, we apply the above methodology to the solution of several tests problems. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.faculty | Instituto de Matemática Interdisciplinar (IMI) | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | MCYT | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/17719 | |
| dc.identifier.isbn | 1-4020-7439-5 | |
| dc.identifier.officialurl | http://www.mat.ucm.es/~aramosol/research/publications/2003Ramos.pdf | |
| dc.identifier.relatedurl | http://www.mat.ucm.es | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/60596 | |
| dc.issue.number | 121 | |
| dc.language.iso | eng | |
| dc.page.final | 344 | |
| dc.page.initial | 333 | |
| dc.page.total | 442 | |
| dc.publication.place | Boston | |
| dc.publisher | Kluwer Academic Publishers | |
| dc.relation.ispartofseries | IFIP | |
| dc.relation.projectID | AGL2000-1440-C02-01 | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 517.95 | |
| dc.subject.keyword | Partial diferential equations | |
| dc.subject.keyword | Heat equation | |
| dc.subject.keyword | Burgers equation | |
| dc.subject.keyword | Optimal control | |
| dc.subject.keyword | Pointwise control | |
| dc.subject.keyword | Nash equilibria | |
| dc.subject.keyword | Adjoint systems | |
| dc.subject.keyword | Conjugate gradient methods | |
| dc.subject.keyword | multiobjective optimization | |
| dc.subject.keyword | Quasi-Newton algorithms. | |
| dc.subject.ucm | Análisis matemático | |
| dc.subject.unesco | 1202 Análisis y Análisis Funcional | |
| dc.title | Numerical methods for Nash equilibria in multiobjective control of partial differential equations | |
| dc.type | book part | |
| dcterms.references | Bristeau, M.O., Glowinski, R., Mantel, B., Periaux, J., and Sefrioui,M., Genetic Algorithms for Electromagnetic Backscattering Multiobjective Opti-mization. In Electromagnetic Optimization by Genetic Algorithms, Edited by Y.Rahmat-Samii and E. Michielssen, John Wiley, New York, pp. 399{434, 1999. Diaz, J.I. and Lions, J.L., On the Approximate Controllability of Stackel-berg-Nash Strategies. In Mathematics and Environment, Lecture Notes, Springer-Verlag, 2001. Lions, J.L., Controle de Pareto de Systemes Distribues: Le Cas d'Evolution,Comptes Rendus de l'Academie des Sciences, Serie I, 302, 413{417, 1986. Lions, J.L. Some Remarks on Stackelberg's Optimization,Mathematical Models and Methods in Applied Sciences, 4, 477{487, 1994. Liu, D.C., and Nocedal, J., On the Limited Memorey BFGS Method for Large-Scale Optimization, Mathematical Programming, 45, 503{528, 1989. Nash, J.F., Noncooperative Games, Annals of Mathematics,54, 286{295, 1951. Pareto, V., Cours d`Economie Politique, Rouge, Lausanne,Switzerland, 1896. Ramos, A.M., Glowinski, R., and Periaux, J., Nash Equilibria for the Mul-tiobjective Control of Linear Partial Differential Equations, Journal of Optimiza-tion, Theory and Applications, 112, No. 3, 457-498, 2002. Ramos, A.M., Glowinski, R., and Periaux, J., Pointwise Control of the Burgers Equation and Related Nash Equilibrium Problems: Computational Approach,Journal of Optimization, Theory and Applications, 112, No. 3, 499-516, 2002. Von Stackelberg, H., Marktform und Gleichgewicht, Springer, Berlin, Ger-many, 1934. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 581c3cdf-f1ce-41e0-ac1e-c32b110407b1 | |
| relation.isAuthorOfPublication.latestForDiscovery | 581c3cdf-f1ce-41e0-ac1e-c32b110407b1 |
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