Optimal control of systems governed by variational inequalities

  • J. P. Yvon
Optimal Control
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3)


In many physical situations, systems are not represented by equations but by variationnal inequalities : a typical case is systems involving semi-porous mediums but there are many other examples (cf. e.g. Duvaut-Lions [4]). This paper (1) is devoted to the study of optimal control problems for such systems. As in the case of partial differential equations we are led to consider the analogous separation between elliptic and parabolic systems ; this is studied first and then we give two algorithms with application to a biochemical-example.


Hilbert Space Cost Function Variational Inequality Optimal Control Problem Convex Subset 


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  1. (1).
    D. Begis H. Glowinski "Dual num. meth. for some variational problem..." in Techniques of optimization. Academic Press (1972).Google Scholar
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    H. Brezis "Problèmes unilatéraux", Journal of Math. pures et appliquées 51, (1972).Google Scholar
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    J. Cea R. Glowinski J.C. Nedelec "Minimisation de fonctionnelles non différentiables", Proceedings of the Dundee Num. Anal. Symp. (1972).Google Scholar
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    G. Duvaut J.L. Lions "Les inéquations en mécanique et en physique", Dunod Paris (1972)Google Scholar
  5. (5).
    J.P. Kernevez "Evolution et contrôle des systèmes bio-mathématiques" Thèse, Paris (1972).Google Scholar
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    J.L. Lions G. Stampacchia "Variational Inequalities", Comm. on pure and app. math. vol XX, pp. 439–519 (1967).Google Scholar
  7. (7).
    F. Mignot Séminaire Lions-Brezis Paris 1972–1973.Google Scholar
  8. (8).
    J.P. Yvon Thèse Paris 1973.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1973

Authors and Affiliations

  • J. P. Yvon
    • 1
  1. 1.Iria 78RocquencourtFrance

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