메뉴 건너뛰기




Volumn 46, Issue 4, 2007, Pages 1239-1276

A curse-of-dimensionality-free numerical method for solution of certain HJB PDES

Author keywords

Curse of dimensionality; Dynamic programming; Fenchel transform; Hamilton Jacobi Bellman equations; Idempotent analysis; Legendre transform; Max plus algebra; Partial differential equations; Semiconvexity

Indexed keywords

APPLIED MATHEMATICS; CURSE OF DIMENSIONALITY; FIRST ORDERS; HAMILTON-JACOBI-BELLMAN; HAMILTONIAN; INTEGRAL OPERATORS; NONLINEAR CONTROL PROBLEMS; PARTIAL DIFFERENTIAL; SEMI GROUPS; SEMIGROUPS; TIME OPTIMAL CONTROL PROBLEMS;

EID: 48249087688     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/040610830     Document Type: Article
Times cited : (126)

References (42)
  • 4
    • 0001678817 scopus 로고    scopus 로고
    • Markov chain approximations for deterministic control problems with affine dynamics and quadratic cost in the control
    • M. BOUÉ AND P. DUPUIS, Markov chain approximations for deterministic control problems with affine dynamics and quadratic cost in the control, SIAM J. Numer. Anal., 36 (1999), pp. 667-695.
    • (1999) SIAM J. Numer. Anal , vol.36 , pp. 667-695
    • BOUÉ, M.1    DUPUIS, P.2
  • 5
    • 0141439533 scopus 로고
    • A domain decomposition method for Bellman equations
    • F. CAMILLI, M. FALCONE. P. LANUCARA, AND A. SEGHINI, A domain decomposition method for Bellman equations, Contemp. Math., 180 (1994), pp. 477-483.
    • (1994) Contemp. Math , vol.180 , pp. 477-483
    • CAMILLI, F.1    FALCONE, M.2    LANUCARA, P.3    SEGHINI, A.4
  • 6
    • 11144350063 scopus 로고    scopus 로고
    • An efficient algorithm for Hamilton-Jacobi equations in high dimensions
    • E. CARLINI, M. FALCONE, AND R. FERRETTI, An efficient algorithm for Hamilton-Jacobi equations in high dimensions, Comput. Vis. Sci., 7 (2004), pp. 15-29.
    • (2004) Comput. Vis. Sci , vol.7 , pp. 15-29
    • CARLINI, E.1    FALCONE, M.2    FERRETTI, R.3
  • 8
    • 0742285656 scopus 로고    scopus 로고
    • Duality and separation theorems in idempotent semimodules
    • G. COHEN. S. GAUBERT. AND J.-P. QUADRAT, Duality and separation theorems in idempotent semimodules, Linear Algebra Appl., 379 (2004), pp. 395-422.
    • (2004) Linear Algebra Appl , vol.379 , pp. 395-422
    • COHEN, G.1    GAUBERT, S.2    QUADRAT, J.-P.3
  • 9
    • 48249126327 scopus 로고    scopus 로고
    • ∞ problems with active control
    • Optimal Control, Stabilization and Nonsmooth Analysis, M. S. de Queiroz, M. Malisoff, and P. Wolenski, eds, Springer, Berlin
    • ∞ problems with active control, in Optimal Control, Stabilization and Nonsmooth Analysis, Lecture Notes in Control and Inform. Sci. 301, M. S. de Queiroz, M. Malisoff, and P. Wolenski, eds., Springer, Berlin, 2004, pp. 101-120.
    • (2004) Lecture Notes in Control and Inform. Sci , vol.301 , pp. 101-120
    • COLLINS, G.1    MCENEANEY, W.M.2
  • 10
    • 84972545750 scopus 로고
    • Uniqueness of viscosity solutions of Hamilton-Jacobi equations revisited
    • M. G. CRANDALL. H. ISHII. AND P.-L. LIONS, Uniqueness of viscosity solutions of Hamilton-Jacobi equations revisited, J. Math. Soc. Japan, 39 (1987). pp. 581-595.
    • (1987) J. Math. Soc. Japan , vol.39 , pp. 581-595
    • CRANDALL, M.G.1    ISHII, H.2    LIONS, P.-L.3
  • 11
    • 84967758647 scopus 로고
    • Viscosity solutions of Hamilton-Jacobi equations
    • M. G. CRANDALL AND P.-L. LIONS, Viscosity solutions of Hamilton-Jacobi equations. Trans. Amer. Math. Soc., 277 (1983), pp. 1-42.
    • (1983) Trans. Amer. Math. Soc , vol.277 , pp. 1-42
    • CRANDALL, M.G.1    LIONS, P.-L.2
  • 12
    • 0022693379 scopus 로고
    • On existence and uniqueness of solutions of Hamilton-Jacobi equations
    • M. G. CRANDALL AND P.-L. LIONS, On existence and uniqueness of solutions of Hamilton-Jacobi equations, Nonlinear Anal. Theory Appl., 10 (1986), pp. 353-370.
    • (1986) Nonlinear Anal. Theory Appl , vol.10 , pp. 353-370
    • CRANDALL, M.G.1    LIONS, P.-L.2
  • 14
    • 0036105139 scopus 로고    scopus 로고
    • Convergence of the optimal feedback policies in a numerical method for a class of deterministic optimal control problems
    • P. DUPUIS AND A. SZPIRO, Convergence of the optimal feedback policies in a numerical method for a class of deterministic optimal control problems, SIAM J. Control Optim., 40 (2001), pp. 393-420.
    • (2001) SIAM J. Control Optim , vol.40 , pp. 393-420
    • DUPUIS, P.1    SZPIRO, A.2
  • 16
    • 0000504721 scopus 로고    scopus 로고
    • Convergence analysis for a class of high,-order semi-Lagrangian advection schemes
    • M. FALCONE AND R. FERRETTI, Convergence analysis for a class of high,-order semi-Lagrangian advection schemes, SIAM J. Numer. Anal., 35 (1998), pp. 909-940.
    • (1998) SIAM J. Numer. Anal , vol.35 , pp. 909-940
    • FALCONE, M.1    FERRETTI, R.2
  • 17
    • 21144454557 scopus 로고    scopus 로고
    • Max-plus stochastic processes
    • W. H. FLEMING, Max-plus stochastic processes, Appl. Math. Optim., 49 (2004), pp. 159-181.
    • (2004) Appl. Math. Optim , vol.49 , pp. 159-181
    • FLEMING, W.H.1
  • 19
    • 0000873359 scopus 로고    scopus 로고
    • A max-plus-based algorithm for a Hamilton-Jacobi-Bellman equation of nonlinear filtering
    • W. H. FLEMING AND W. M. MCENEANEY, A max-plus-based algorithm for a Hamilton-Jacobi-Bellman equation of nonlinear filtering, SIAM J. Control Optim., 38 (2000), pp. 683-710.
    • (2000) SIAM J. Control Optim , vol.38 , pp. 683-710
    • FLEMING, W.H.1    MCENEANEY, W.M.2
  • 26
    • 0012074126 scopus 로고    scopus 로고
    • Idempotent functional analysis: An algebraic approach
    • G. L. LITVINOV, V. P. MASLOV. AND G. B. SHPIZ, Idempotent functional analysis: An algebraic approach, Math. Notes, 69 (2001), pp. 696-729.
    • (2001) Math. Notes , vol.69 , pp. 696-729
    • LITVINOV, G.L.1    MASLOV, V.P.2    SHPIZ, G.B.3
  • 27
    • 0001866020 scopus 로고
    • On a new principle of superposition for optimization problems
    • V. P. MASLOV, On a new principle of superposition for optimization problems, Russian Math. Surveys, 42 (1987), pp. 43-54.
    • (1987) Russian Math. Surveys , vol.42 , pp. 43-54
    • MASLOV, V.P.1
  • 29
    • 33847042707 scopus 로고    scopus 로고
    • Max-plus summation of Fenchel-transformed semigroups for solution of nonlinear Bellman equations
    • W. M. MCENEANEY, Max-plus summation of Fenchel-transformed semigroups for solution of nonlinear Bellman equations, Systems Control Lett., 56 (2007), pp. 255-264.
    • (2007) Systems Control Lett , vol.56 , pp. 255-264
    • MCENEANEY, W.M.1
  • 31
    • 16244396125 scopus 로고    scopus 로고
    • ∞ problems: Error analysis
    • ∞ problems: Error analysis, SIAM J. Control Optim., 43 (2004), pp. 379-412.
    • (2004) SIAM J. Control Optim , vol.43 , pp. 379-412
    • MCENEANEY, W.M.1
  • 33
    • 48249120256 scopus 로고    scopus 로고
    • W. M. MCENEANEY, Error analysis of a max-plus algorithm for a first-order HJB equation, in Stochastic Theory and Control, Proceedings of a Workshop held in Lawrence, KS, October 18-20, 2001, B. Pasik-Duncan, ed., Lecture Notes in Control and Inform. Sci., Springer-Verlag, New York, 2002, pp. 335-352.
    • W. M. MCENEANEY, Error analysis of a max-plus algorithm for a first-order HJB equation, in Stochastic Theory and Control, Proceedings of a Workshop held in Lawrence, KS, October 18-20, 2001, B. Pasik-Duncan, ed., Lecture Notes in Control and Inform. Sci., Springer-Verlag, New York, 2002, pp. 335-352.
  • 36
    • 0347606272 scopus 로고    scopus 로고
    • ∞ control
    • International Federation of Automatic Control, Pergamon Press, Oxford
    • ∞ control, in Proceedings of the 13th World Congress, International Federation of Automatic Control, Pergamon Press, Oxford, 1996, pp. 401-406.
    • (1996) Proceedings of the 13th World Congress , pp. 401-406
    • MCENEANEY, W.M.1    DAY, M.V.2
  • 38
    • 48249134630 scopus 로고    scopus 로고
    • R. T. ROCKAFELLAR, Conjugate Duality and Optimization, CBMS-NSF Reg. Conf. Ser. Appl. Math. 16, SIAM, Philadelphia, 1974.
    • R. T. ROCKAFELLAR, Conjugate Duality and Optimization, CBMS-NSF Reg. Conf. Ser. Appl. Math. 16, SIAM, Philadelphia, 1974.
  • 40
    • 0030151815 scopus 로고    scopus 로고
    • ∞ control of nonlinear systems: Differential games and viscosity solutions
    • ∞ control of nonlinear systems: Differential games and viscosity solutions, SIAM J. Control Optim., 34 (1996), pp. 1071-1097.
    • (1996) SIAM J. Control Optim , vol.34 , pp. 1071-1097
    • SORAVIA, P.1
  • 41
    • 0038380608 scopus 로고    scopus 로고
    • Second order numerical methods for first order Hamilton-Jacobi equations
    • A. SZPIRO AND P. DUPUIS, Second order numerical methods for first order Hamilton-Jacobi equations, SIAM J. Numer. Anal., 40 (2002), pp. 1136-1183,
    • (2002) SIAM J. Numer. Anal , vol.40 , pp. 1136-1183
    • SZPIRO, A.1    DUPUIS, P.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.