Least regret control, virtual control and decomposition methods

Jacques-Louis Lions

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2000)

  • Volume: 34, Issue: 2, page 409-418
  • ISSN: 0764-583X

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Lions, Jacques-Louis. "Least regret control, virtual control and decomposition methods." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 34.2 (2000): 409-418. <http://eudml.org/doc/193993>.

@article{Lions2000,
author = {Lions, Jacques-Louis},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {least regret control; virtual control; domain decomposition; second-order elliptic operator; quadratic functional; optimal control; algorithm},
language = {eng},
number = {2},
pages = {409-418},
publisher = {Dunod},
title = {Least regret control, virtual control and decomposition methods},
url = {http://eudml.org/doc/193993},
volume = {34},
year = {2000},
}

TY - JOUR
AU - Lions, Jacques-Louis
TI - Least regret control, virtual control and decomposition methods
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2000
PB - Dunod
VL - 34
IS - 2
SP - 409
EP - 418
LA - eng
KW - least regret control; virtual control; domain decomposition; second-order elliptic operator; quadratic functional; optimal control; algorithm
UR - http://eudml.org/doc/193993
ER -

References

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  1. [1] A. Bensoussan, J.L. Lions and R. Temam, Sur les méthodes de décomposition, de décentralisation et de coordination et applications, Méthodes Mathématiques de l'Informatique, J.L. Lions and G.I. Marchuk Eds, Dunod, Paris (1974) 133-257. Zbl0275.90042
  2. [2] I. Ekeland and R. Temam, Analyse convexe et problèmes variationnels, Dunod, Gauthier-Villars (1974). Zbl0281.49001MR463993
  3. [3] D. Gabay and J.L. Lions, Décisions stratégiques à moindres regrets. C.R. Acad. Sci. Paris 319 (1994) 1049-1056. Zbl0819.90002MR1305675
  4. [4] R. Glowinski and J.L. Lions, Exact and approximate controllability for distributed parameter systems. Acta Numer. (1994) 269-378 and (1995) 159-333. Zbl0838.93014MR1352473
  5. [5] R. Glowinski, J.L. Lionsand O. Pironneau, Decomposition of energy spaces and applications. C.R. Acad. Sci. Paris 329 (1999) 445-452. Zbl0938.65081MR1710079
  6. [6] J.L. Lions, Contrôle optimal des systèmes gouvernés par des équations aux dérivées partielles, Paris, Dunod, Gauthier-Villars (1968). Zbl0179.41801MR244606
  7. [7] J.L. Lions, Contrôle à moindres regrets des systèmes distribués. C.R. Acad. Sci. Paris 315 (1992) 1253-1257. Zbl0766.93033MR1194529
  8. [8] J.L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, Dunod, Paris (1968) Vol. 1 and 2. Zbl0165.10801
  9. [9] J.L. Lions and O. Pironneau, Algorithmes parallèles pour la solution de problèmes aux limites. C.R. Acad. Sci. Paris 327 (1998) 947-952. Zbl0918.65071MR1659169
  10. [10] J.L. Lions and O. Pironneau, Domain decomposition methods for CAD. C.R. Acad. Sci. Paris 328 (1999) 73-80. Zbl0937.68140MR1674382
  11. [11] J.L. Lions and O. Pironneau, Décomposition d'opérateurs, répliques et contrôle virtuel. C.R. Acad. Sci. Paris (to appear). 
  12. [12] J.L. Lions and O. Pironneau, Sur le contrôle parallèle de systèmes distribués. C.R. Acad. Sci. Paris 327 (1998) 993-998. Zbl0926.93032MR1659213
  13. [13] L.J. Savage, The foundations of Statistics, 2nd edition, Dover (1972). Zbl0276.62006MR348870

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