Minimax solutions of the dual Hamilton-Jacobi equation

• Autorzy: Nowakowski A.
• Języki publikacji: EN

Abstrakty

EN

In the paper the existence and continuous dependence of a kind of minimax solution to the dual Hamilton-Jacobi equations is proved. The main difficulties which appear here are a special type of the boundary conditions and the transversality conditions which that solution must satisfy. That type of problems come from optimal control and game theory.

Słowa kluczowe

EN

dual Hamilton-Jacobi equation; minimax solutions; generalized solutions; generalized problem of Bolza

PL

podwójne równanie Hamilton-Jacobi; minimax rozwiązań; rozwiązania uogólnione; uogólniony problem Bolza

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2003
• Tom: Vol. 9, nr 1
• Strony: 75--102
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Nowakowski A.

• Faculty of Mathematics University of Łódź Banacha 22 90-238 Łódź, Poland,

Bibliografia

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• [3] Frankowska, H., Plaskacz, S., Semicontinuous solutions of Hamilton-Jacobi-Bellman equations with state constraints, Cahiers Centre Rech. Viab. Jeux Control 9809 (1998).
• [4] Lions, P. L., Optimal Control and Viscosity Solutions, Lecture Notes in Math. 1119, Springer, Berlin, 1985.
• [5] Lions, P. L., Neuman type boundary conditions for Hamilton-Jacobi equations, Duke Math. J. 52 (1985), 793-820.
• [6] Nowakowska, L, Dual Game Theory and Its Applications in Economic, PhD thesis, Univ. Łódź, Department of Statistics, Łódź, 1998.
• [7] Nowakowski, A., Field theories in the modem calculus of variations, Trans. Amer. Math. Soc. 309 (1988), 725-752.
• [8] Nowakowski, A., The dual dynamic programming, Proc. Amer. Math. Soc. 116 (1992), 1089-1096.
• [9] Sobieski, S., Dual Approach to Game Theory, PhD thesis, Univ. Łódź, Faculty of Mathematics, Łódź, 2002.
• [10] Subbotin, A. L, Minimax Inequalities and Hamilton-Jacobi Equations, Nauka, Moscow, 1991.