On Porter's pursuit-evasion games

  • J. Fichefet
Contributed Papers

Abstract

A minimax problem for Porter's class of functionals is considered in the case when the two players' strategies are elements of convex and strongly or weakly compact subsets of real Hilbert spaces. Functional analysis is used to prove sufficient conditions ensuring the existence of saddle points. An example illustrates the results, and a necessary condition of optimality of strategies is given in a particular case.

Keywords

Hilbert Space Functional Analysis Saddle Point Compact Subset Real Hilbert Space 

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References

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    Porter, W. A.,On Function Space Pursuit-Evasion Games, SIAM Journal on Control, Vol. 5, No. 4, 1967.Google Scholar
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    Sion, M.,On General Minimax Theorems, Pacific Journal of Mathematics, Vol. 8, No. 1, 1958.Google Scholar
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    Sakawa, Y.,On Linear Differential Games, Mathematical Theory of Control, Edited by A. V. Balakrishnan and L. W. Neustadt, Academic Press, New York, 1967.Google Scholar
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    Fichefet, J.,Quelques Conditions d'Existence de Points de Selle pour une Classe de Jeux Différentiels de Durée Fixée, Centre Belge de Recherches Mathématiques, Colloque sur la Théorie Mathématique du Contrôle Optimal (to appear).Google Scholar
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    Hurwicz, L.,Programming in Linear Spaces, Studies in Linear and Nonlinear Programming, Edited by K. J. Arrow, L. Hurwicz, and H. Uzawa, Stanford University Press, Stanford, California, 1958.Google Scholar

Copyright information

© Plenum Publishing Corporation 1970

Authors and Affiliations

  • J. Fichefet
    • 1
  1. 1.Computation LaboratoryFree University of BrusselsBrusselsBelgium

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