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Volumn 36, Issue 3, 1998, Pages 1048-1072

Proximal analysis and the minimal time function

Author keywords

Continuity of value functions; Hamilton Jacobi equations; Minimal time function; Nonsmooth analysis; Proximal analysis

Indexed keywords

BOUNDARY CONDITIONS; FUNCTIONS;

EID: 0032070810     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012996299338     Document Type: Article
Times cited : (92)

References (40)
  • 2
    • 0024705092 scopus 로고
    • A boundary value problem for the minimum-time function
    • M. BARDI, A boundary value problem for the minimum-time function, SIAM J. Control Optim., 27 (1989), pp. 776-785.
    • (1989) SIAM J. Control Optim. , vol.27 , pp. 776-785
    • Bardi, M.1
  • 3
    • 0007015652 scopus 로고
    • The Bellman equation for time-optimal control of noncontrollable nonlinear systems
    • M. BARDI AND V. STAICU, The Bellman equation for time-optimal control of noncontrollable nonlinear systems, Acta Appl. Math., 31 (1993), pp. 201-223.
    • (1993) Acta Appl. Math. , vol.31 , pp. 201-223
    • Bardi, M.1    Staicu, V.2
  • 4
    • 0025462851 scopus 로고
    • An approximation scheme for the minimum time function
    • M. BARDI AND M. FALCONE, An approximation scheme for the minimum time function, SIAM J. Control Qptim., 28 (1990), pp. 950-965.
    • (1990) SIAM J. Control Qptim. , vol.28 , pp. 950-965
    • Bardi, M.1    Falcone, M.2
  • 5
    • 84968515664 scopus 로고
    • Optimal control and semicontinuous viscosity solutions
    • E. N. BARRON AND R. JENSEN, Optimal control and semicontinuous viscosity solutions, Proc. Amer. Math. Soc., 113 (1991), pp. 397-402.
    • (1991) Proc. Amer. Math. Soc. , vol.113 , pp. 397-402
    • Barron, E.N.1    Jensen, R.2
  • 6
    • 78049400271 scopus 로고
    • Semicontinuous viscosity solutions for Hamilton-Jacobi equations with convex Hamiltonians
    • E. N. BARRON AND R. JENSEN, Semicontinuous viscosity solutions for Hamilton-Jacobi equations with convex Hamiltonians, Comm. Partial Differential Equations, 15 (1990), pp. 1713-1742.
    • (1990) Comm. Partial Differential Equations , vol.15 , pp. 1713-1742
    • Barron, E.N.1    Jensen, R.2
  • 8
    • 21844502491 scopus 로고
    • Lower semicontinuous solutions of the Bellman equation for the minimal time problem
    • O. CARJA, F. MIGNANEGO, AND G. PIERI, Lower semicontinuous solutions of the Bellman equation for the minimal time problem, J. Optim. Theory Appl., 85 (1995), pp. 563-574.
    • (1995) J. Optim. Theory Appl. , vol.85 , pp. 563-574
    • Carja, O.1    Mignanego, F.2    Pieri, G.3
  • 9
    • 0000596189 scopus 로고
    • Optimization and Nonsmooth Analysis
    • SIAM, Philadelphia, (Originally published by Wiley Interscience, New York, 1983)
    • F. H. CLARKE, Optimization and Nonsmooth Analysis, Classics Appl. Math. 5, SIAM, Philadelphia, 1990. (Originally published by Wiley Interscience, New York, 1983.)
    • (1990) Classics Appl. Math. , vol.5
    • Clarke, F.H.1
  • 10
    • 0003225812 scopus 로고
    • Methods of Dynamic and Nonsmooth Optimization
    • SIAM, Philadelphia
    • F. H. CLARKE. Methods of Dynamic and Nonsmooth Optimization, CBMS-NSF Regional Conf. Ser. in Appl. Math. 57, SIAM, Philadelphia, 1989.
    • (1989) CBMS-NSF Regional Conf. Ser. in Appl. Math. , vol.57
    • Clarke, F.H.1
  • 11
    • 84968476212 scopus 로고
    • Mean value inequalities in Hilbert space
    • F. H. CLARKE AND YU. S. LEDYAEV, Mean value inequalities in Hilbert space, Trans. Amer. Math. Soc., 344 (1994), pp. 307-324.
    • (1994) Trans. Amer. Math. Soc. , vol.344 , pp. 307-324
    • Clarke, F.H.1    Ledyaev, Yu.S.2
  • 15
    • 0000585951 scopus 로고
    • Subgradient criteria for monotonicity, the Lipschitz condition, and convexity
    • F. H. CLARKE. R. J. STERN, AND P. R. WOLENSKI, Subgradient criteria for monotonicity, the Lipschitz condition, and convexity, Canad. J. Math., 45 (1983), pp. 1167-1183.
    • (1983) Canad. J. Math. , vol.45 , pp. 1167-1183
    • Clarke, F.H.1    Stern, R.J.2    Wolenski, P.R.3
  • 17
    • 0020843419 scopus 로고
    • Local optimality conditions and Lipschitzian solutions to the Hamilton-Jacobi equation
    • F. H. CLARKE AND R. B. VINTER, Local optimality conditions and Lipschitzian solutions to the Hamilton-Jacobi equation, SIAM J. Control Optim., 21 (1983), pp. 856-870.
    • (1983) SIAM J. Control Optim. , vol.21 , pp. 856-870
    • Clarke, F.H.1    Vinter, R.B.2
  • 18
    • 0030555288 scopus 로고    scopus 로고
    • Control of systems to sets and their interiors
    • F. H. CLARKE AND P. R. WOLENSKI, Control of systems to sets and their interiors, J. Optim. Theory Appl., 88 (1996), pp. 3-23.
    • (1996) J. Optim. Theory Appl. , vol.88 , pp. 3-23
    • Clarke, F.H.1    Wolenski, P.R.2
  • 19
    • 84967708673 scopus 로고
    • User's guide to viscosity solutions of second order partial differential equations
    • M. G. CRANDALL, H. ISHII, AND P.-L. LIONS, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc., 27 (1992), pp. 1-67.
    • (1992) Bull. Amer. Math. Soc. , vol.27 , pp. 1-67
    • Crandall, M.G.1    Ishii, H.2    Lions, P.-L.3
  • 20
    • 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
  • 21
    • 0024771431 scopus 로고
    • The Hamilton-Jacobi-Bellman equation for time-optimal control
    • L. C. EVANS AND M. R. JAMES, The Hamilton-Jacobi-Bellman equation for time-optimal control, SIAM J. Control Optim., 27 (1989), pp. 1477-1489.
    • (1989) SIAM J. Control Optim. , vol.27 , pp. 1477-1489
    • Evans, L.C.1    James, M.R.2
  • 23
    • 0000706858 scopus 로고
    • Classical solutions of differential equations with multivalued right-hand side
    • A. F. FILIPPOV, Classical solutions of differential equations with multivalued right-hand side, SIAM J. Control Optim., 5 (1967), pp. 609-621.
    • (1967) SIAM J. Control Optim. , vol.5 , pp. 609-621
    • Filippov, A.F.1
  • 24
    • 85066086057 scopus 로고
    • Lower semicontinuous solutions of the Hamilton-Jacobi equation
    • H. FRANKOWSKA, Lower semicontinuous solutions of the Hamilton-Jacobi equation, SIAM J. Control Optim., 31 (1993), pp. 257-272.
    • (1993) SIAM J. Control Optim. , vol.31 , pp. 257-272
    • Frankowska, H.1
  • 25
    • 0003239028 scopus 로고
    • Optimal Control via Nonsmooth Analysis
    • AMS, Providence, RI
    • P. D. LOEWEN, Optimal Control via Nonsmooth Analysis, CRM Proc. Lecture Notes 2, AMS, Providence, RI, 1993.
    • (1993) CRM Proc. Lecture Notes , vol.2
    • Loewen, P.D.1
  • 26
    • 0040782372 scopus 로고
    • On the Bellman function for the time optimal process problem
    • N. N. PETROV, On the Bellman function for the time optimal process problem, J. Appl. Math. Mech., 34 (1970), pp. 785-791.
    • (1970) J. Appl. Math. Mech. , vol.34 , pp. 785-791
    • Petrov, N.N.1
  • 27
    • 0000752102 scopus 로고
    • Proximal subgradients, marginal values, and augmented Lagrangians in nonconvex optimization
    • R. T. ROCKAFELLAR, Proximal subgradients, marginal values, and augmented Lagrangians in nonconvex optimization, Math. Oper. Res., 6 (1981), pp. 424-436.
    • (1981) Math. Oper. Res. , vol.6 , pp. 424-436
    • Rockafellar, R.T.1
  • 29
    • 0027590036 scopus 로고
    • Pursuit-evasion problems and viscosity solutions of Isaacs equations
    • P. SORAVIA, Pursuit-evasion problems and viscosity solutions of Isaacs equations, SIAM J. Control Optim., 31 (1993), pp. 604-623.
    • (1993) SIAM J. Control Optim. , vol.31 , pp. 604-623
    • Soravia, P.1
  • 30
    • 0001426381 scopus 로고
    • Discontinuous viscosity solutions to Dirichlet problems for Hamilton-Jacobi equations with convex Hamiltonians
    • P. SORAVIA, Discontinuous viscosity solutions to Dirichlet problems for Hamilton-Jacobi equations with convex Hamiltonians, Comm. Partial Differential Equations, 18 (1993), pp. 1493-1514.
    • (1993) Comm. Partial Differential Equations , vol.18 , pp. 1493-1514
    • Soravia, P.1
  • 31
    • 38149148188 scopus 로고
    • Generalized motion of a front propagating along its normal direction: A differential games approach
    • P. SORAVIA, Generalized motion of a front propagating along its normal direction: A differential games approach, Nonlinear Anal., 22 (1994), pp. 1247-1262.
    • (1994) Nonlinear Anal. , vol.22 , pp. 1247-1262
    • Soravia, P.1
  • 32
    • 1542714069 scopus 로고
    • Minimal time function and viscosity solutions
    • V. STAICU, Minimal time function and viscosity solutions, J. Optim. Theory Appl., 60 (1989), pp. 81-91.
    • (1989) J. Optim. Theory Appl. , vol.60 , pp. 81-91
    • Staicu, V.1
  • 33
    • 0001689069 scopus 로고
    • A generalization of the basic equation of the theory of differential games
    • A. I. SUBBOTIN, A generalization of the basic equation of the theory of differential games, Soviet Math. Dokl., 22 (1980), pp. 358-362.
    • (1980) Soviet Math. Dokl. , vol.22 , pp. 358-362
    • Subbotin, A.I.1
  • 34
    • 0021422727 scopus 로고
    • Generalization of the main equation of differential games
    • A. I. SUBBOTIN, Generalization of the main equation of differential games, J. Optim. Theory Appl., 43 (1984), pp. 103-133.
    • (1984) J. Optim. Theory Appl. , vol.43 , pp. 103-133
    • Subbotin, A.I.1
  • 35
    • 0023138986 scopus 로고
    • A general theorem on local controllability
    • H. J. SUSSMANN, A general theorem on local controllability, SIAM J. Control Optim., 25 (1987), pp. 158-194.
    • (1987) SIAM J. Control Optim. , vol.25 , pp. 158-194
    • Sussmann, H.J.1
  • 36
    • 0009557401 scopus 로고
    • Sufficient conditions for viability under imperfect measurement
    • V. VELIOV, Sufficient conditions for viability under imperfect measurement, Set-Valued Anal., 1 (1993), pp. 305-317.
    • (1993) Set-Valued Anal. , vol.1 , pp. 305-317
    • Veliov, V.1
  • 37
    • 0031528002 scopus 로고    scopus 로고
    • Lipschitz Continuity of the Value Function in Optimal Control
    • V. VELIOV, Lipschitz Continuity of the Value Function in Optimal Control, J. Optim. Theory Appl., 94 (1997), pp. 335-363.
    • (1997) J. Optim. Theory Appl. , vol.94 , pp. 335-363
    • Veliov, V.1
  • 38
    • 38249020186 scopus 로고
    • A uniqueness theorem for differential inclusions
    • P. R. WOLENSKI, A uniqueness theorem for differential inclusions, J. Differential Equations, 84 (1990), pp. 165-182.
    • (1990) J. Differential Equations , vol.84 , pp. 165-182
    • Wolenski, P.R.1
  • 39
    • 0025483554 scopus 로고
    • The exponential formula for the reachable set of a Lipschitz differential inclusion
    • P. R. WOLENSKI, The exponential formula for the reachable set of a Lipschitz differential inclusion, SIAM J. Control Optim., 28 (1990), pp. 1148-1161.
    • (1990) SIAM J. Control Optim. , vol.28 , pp. 1148-1161
    • Wolenski, P.R.1


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