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Volumn 26, Issue 8, 1996, Pages 1429-1436

Sub- and superoptimality principles of dynamic programming revisited

Author keywords

Differential games; Dynamic programming; Hamilton Jacobi Bellman Isaacs equations; Optimality principles; Viscosity solutions

Indexed keywords

CALCULATIONS; CONTROL THEORY; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); FUNCTIONS; GAME THEORY; OPTIMAL CONTROL SYSTEMS; OPTIMIZATION; SET THEORY; THEOREM PROVING;

EID: 0030127283     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/0362-546X(94)00348-L     Document Type: Article
Times cited : (14)

References (18)
  • 1
    • 84947513018 scopus 로고
    • Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations, Parts 1, 2
    • LIONS, P. L., Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations, Parts 1, 2, Communs partial diff. Eqns 8, 1101-1174, 1229-1276 (1983).
    • (1983) Communs Partial Diff. Eqns , vol.8 , pp. 1101-1174
    • Lions, P.L.1
  • 2
    • 0021453741 scopus 로고
    • Differential games, optimal control and directional derivatives of viscosity solutions of Bellman's and Isaac's equations
    • LIONS P. L. & SOUGANIDIS P. E., Differential games, optimal control and directional derivatives of viscosity solutions of Bellman's and Isaac's equations, SIAM J. Control Optim. 23, 566-583 (1985).
    • (1985) SIAM J. Control Optim. , vol.23 , pp. 566-583
    • Lions, P.L.1    Souganidis, P.E.2
  • 3
    • 84967758647 scopus 로고
    • Viscosity solutions of Hamilton-Jacobi equations
    • CRANDALL M. G. & LIONS P. L., Viscosity solutions of Hamilton-Jacobi equations, Trans. Am. math. Soc. 277, 1-42 (1983).
    • (1983) Trans. Am. Math. Soc. , vol.277 , pp. 1-42
    • Crandall, M.G.1    Lions, P.L.2
  • 4
    • 84967708673 scopus 로고
    • User's guide to viscosity solutions of second order partial differential equations
    • CRANDALL M. G., ISHII H. & LIONS P. L., User's guide to viscosity solutions of second order partial differential equations, Bull. Am. math. Soc. 27, 1-67 (1992).
    • (1992) Bull. Am. Math. Soc. , vol.27 , pp. 1-67
    • Crandall, M.G.1    Ishii, H.2    Lions, P.L.3
  • 9
    • 0001391958 scopus 로고
    • Optimal trajectories associated to a solution of contingent Hamilton-Jacobi equation
    • FRANKOWSKA H., Optimal trajectories associated to a solution of contingent Hamilton-Jacobi equation, Appl. Math. Optim. 19, 291-311 (1989).
    • (1989) Appl. Math. Optim. , vol.19 , pp. 291-311
    • Frankowska, H.1
  • 10
    • 85066086057 scopus 로고
    • Lower semicontinuous solutions of Hamilton-Jacobi-Bellman equations
    • FRANKOWSKA H., Lower semicontinuous solutions of Hamilton-Jacobi-Bellman equations, SIAM J. Control. Optim. 31, 257-272 (1993).
    • (1993) SIAM J. Control. Optim. , vol.31 , pp. 257-272
    • Frankowska, H.1
  • 12
    • 51249173208 scopus 로고
    • A remark on regularization in Hilbert spaces
    • LASRY J. M. & LIONS P. L., A remark on regularization in Hilbert spaces, Israel J. Math. 55, 257-266 (1986).
    • (1986) Israel J. Math. , vol.55 , pp. 257-266
    • Lasry, J.M.1    Lions, P.L.2
  • 13
    • 84966259849 scopus 로고
    • A uniqueness result for viscosity solutions of second order fully nonlinear partial differential equations
    • JENSEN R., LIONS P. L. & SOUGANIDIS P. E., A uniqueness result for viscosity solutions of second order fully nonlinear partial differential equations, Proc. Am. math. Soc. 102, 975-978 (1988).
    • (1988) Proc. Am. Math. Soc. , vol.102 , pp. 975-978
    • Jensen, R.1    Lions, P.L.2    Souganidis, P.E.3
  • 14
    • 0002638071 scopus 로고
    • The existence of value in differential games
    • ELLIOT R. J. & KALTON N. J., The existence of value in differential games, Mem. Am. math. Soc. 126 (1972).
    • (1972) Mem. Am. Math. Soc. , vol.126
    • Elliot, R.J.1    Kalton, N.J.2
  • 15
    • 0000102846 scopus 로고
    • Differential games and representation formulas for solutions of Hamilton-Jacobi equations
    • EVANS L. C. & SOUGANIDIS P. E., Differential games and representation formulas for solutions of Hamilton-Jacobi equations, Indiana Univ. Math. J. 33 ,773-797 (1984).
    • (1984) Indiana Univ. Math. J. , vol.33 , pp. 773-797
    • Evans, L.C.1    Souganidis, P.E.2
  • 16
    • 0001586443 scopus 로고
    • Differential games with maximum cost
    • BARRON E. N., Differential games with maximum cost, Nonlinear Analysis 14, 971-989 (1990).
    • (1990) Nonlinear Analysis , vol.14 , pp. 971-989
    • Barron, E.N.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.