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Volumn 34, Issue 5, 1996, Pages 1568-1591

Viscosity solutions and viscosity subderivatives in smooth Banach spaces with applications to metric regularity

Author keywords

Fuzzy sum rule; Hamilton Jacobi equations; Metric regularity; Smooth spaces; Viscosity solutions; Viscosity subderivative

Indexed keywords

CONTROL THEORY; NUMERICAL METHODS; PROBLEM SOLVING; VARIATIONAL TECHNIQUES; VISCOSITY;

EID: 0030242650     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012994268801     Document Type: Article
Times cited : (62)

References (49)
  • 2
    • 85033865280 scopus 로고    scopus 로고
    • On a Newton type iterative method for solving inclusions
    • to appear
    • D. AZÉ AND C. C. CHOU, On a Newton type iterative method for solving inclusions, in Math. Oper. Res., to appear.
    • Math. Oper. Res.
    • Azé, D.1    Chou, C.C.2
  • 3
    • 0022465886 scopus 로고
    • Stability and regular points of inequality systems
    • J. M. BORWEIN, Stability and regular points of inequality systems, J. Optim. Theory Appl., 48 (1986), pp. 9-52.
    • (1986) J. Optim. Theory Appl. , vol.48 , pp. 9-52
    • Borwein, J.M.1
  • 4
    • 38249036307 scopus 로고
    • Epi-Lipschitz-like sets in Banach space: Theorems and examples
    • _, Epi-Lipschitz-like sets in Banach space: Theorems and examples, Nonlinear Anal., 11 (1987), pp. 1207-1217.
    • (1987) Nonlinear Anal. , vol.11 , pp. 1207-1217
  • 8
    • 0006419289 scopus 로고
    • Proximal analysis in smooth spaces
    • CECM research report 93-04
    • J. M. BORWEIN AND A. IOFFE, Proximal analysis in smooth spaces, CECM research report 93-04 (1993), to appear in Set-Valued Anal.
    • (1993) Set-Valued Anal.
    • Borwein, J.M.1    Ioffe, A.2
  • 9
    • 84966213239 scopus 로고
    • A smooth variational principle with applications to subdifferentiability and to differentiability of convex functions
    • J. M. BORWEIN AND D. PREISS, A smooth variational principle with applications to subdifferentiability and to differentiability of convex functions, Trans. Ame. Math. Soc., Soc., 303 (1987), pp. 517-527.
    • (1987) Trans. Ame. Math. Soc., Soc. , vol.303 , pp. 517-527
    • Borwein, J.M.1    Preiss, D.2
  • 12
    • 4243049021 scopus 로고
    • Methods of Dynamic and Nonsmooth Optimization
    • Society for Industrial and Applied Mathematics, Philadelphia
    • _, Methods of Dynamic and Nonsmooth Optimization, CBMS-NSF Regional Conf. Ser. in Appl. Math., Society for Industrial and Applied Mathematics, Philadelphia, 1989.
    • (1989) CBMS-NSF Regional Conf. Ser. in Appl. Math.
  • 13
    • 84968507121 scopus 로고
    • Some properties of viscosity solutions of Hamilton-Jacobi equations
    • M. G. CRANDALL, L. C. EVANS, AND P.-L. LIONS, Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc., 282 (1984), pp. 487-502.
    • (1984) Trans. Amer. Math. Soc. , vol.282 , pp. 487-502
    • Crandall, M.G.1    Evans, L.C.2    Lions, P.-L.3
  • 14
    • 84967708673 scopus 로고
    • User's guide to viscosity solutions of second order partial differential equations
    • N.S.
    • 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. (N.S.), 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
  • 15
    • 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
  • 16
    • 46549092471 scopus 로고
    • Hamilton-Jacobi equations in infinite dimensions, Part I. Uniqueness of viscosity solutions
    • _, Hamilton-Jacobi equations in infinite dimensions, Part I. Uniqueness of viscosity solutions, J. Funct. Anal., 62 (1985), pp. 379-396; Part II. Existence of viscosity solutions, 65 (1986), pp. 368-405; Part III, 68 (1986), pp. 214-247; Part IV. Unbounded linear terms, 90 (1990), pp. 237-283; Part V, B-continuous solutions, 97 (1991), pp. 417-465.
    • (1985) J. Funct. Anal. , vol.62 , pp. 379-396
  • 17
    • 46149138623 scopus 로고
    • Existence of viscosity solutions
    • _, Hamilton-Jacobi equations in infinite dimensions, Part I. Uniqueness of viscosity solutions, J. Funct. Anal., 62 (1985), pp. 379-396; Part II. Existence of viscosity solutions, 65 (1986), pp. 368-405; Part III, 68 (1986), pp. 214-247; Part IV. Unbounded linear terms, 90 (1990), pp. 237-283; Part V, B-continuous solutions, 97 (1991), pp. 417-465.
    • (1986) J. Funct. Anal. , vol.65 , Issue.2 PART , pp. 368-405
  • 18
    • 46149127983 scopus 로고
    • _, Hamilton-Jacobi equations in infinite dimensions, Part I. Uniqueness of viscosity solutions, J. Funct. Anal., 62 (1985), pp. 379-396; Part II. Existence of viscosity solutions, 65 (1986), pp. 368-405; Part III, 68 (1986), pp. 214-247; Part IV. Unbounded linear terms, 90 (1990), pp. 237-283; Part V, B-continuous solutions, 97 (1991), pp. 417-465.
    • (1986) J. Funct. Anal. , vol.68 , Issue.3 PART , pp. 214-247
  • 19
    • 44949288472 scopus 로고
    • Unbounded linear terms
    • _, Hamilton-Jacobi equations in infinite dimensions, Part I. Uniqueness of viscosity solutions, J. Funct. Anal., 62 (1985), pp. 379-396; Part II. Existence of viscosity solutions, 65 (1986), pp. 368-405; Part III, 68 (1986), pp. 214-247; Part IV. Unbounded linear terms, 90 (1990), pp. 237-283; Part V, B-continuous solutions, 97 (1991), pp. 417-465.
    • (1990) J. Funct. Anal. , vol.90 , Issue.4 PART , pp. 237-283
  • 20
    • 0001295449 scopus 로고
    • B-continuous solutions
    • _, Hamilton-Jacobi equations in infinite dimensions, Part I. Uniqueness of viscosity solutions, J. Funct. Anal., 62 (1985), pp. 379-396; Part II. Existence of viscosity solutions, 65 (1986), pp. 368-405; Part III, 68 (1986), pp. 214-247; Part IV. Unbounded linear terms, 90 (1990), pp. 237-283; Part V, B-continuous solutions, 97 (1991), pp. 417-465.
    • (1991) J. Funct. Anal. , vol.97 , Issue.5 PART , pp. 417-465
  • 23
    • 0000801656 scopus 로고
    • A smooth variational principle with applications to Hamilton-Jacobi equations in infinite dimensions
    • _, A smooth variational principle with applications to Hamilton-Jacobi equations in infinite dimensions, J. Funct. Anal., 111 (1993), pp. 197-212.
    • (1993) J. Funct. Anal. , vol.111 , pp. 197-212
  • 25
    • 0002348503 scopus 로고
    • On class of subdifferentiability spaces of loffe
    • M. FABIAN, On class of subdifferentiability spaces of loffe, Nonlinear Anal., 12 (1988), pp. 63-74.
    • (1988) Nonlinear Anal. , vol.12 , pp. 63-74
    • Fabian, M.1
  • 27
    • 0006486784 scopus 로고
    • The maximum principle in optimal control of system governed by semilinear equations
    • Proceedings of the IMA Workshop on Nonsmooth Analysis and Geometric Methods in Deterministic Optim. Control, B. S. Mordukhovich and H. T. Sussmann, eds., Springler-Verlag, New York
    • B. GINSBURG AND A. D. IOFFEM The maximum principle in optimal control of system governed by semilinear equations, in Proceedings of the IMA Workshop on Nonsmooth Analysis and Geometric Methods in Deterministic Optim. Control, B. S. Mordukhovich and H. T. Sussmann, eds., IMA Vol. Math. Appl., Springler-Verlag, New York, 1995.
    • (1995) IMA Vol. Math. Appl.
    • Ginsburg, B.1    Ioffem, A.D.2
  • 28
    • 84867959059 scopus 로고
    • Regular points of Lipschitz mappings
    • A. D. IOFFE, Regular points of Lipschitz mappings, Trans. Amer. Math. Soc., 251 (1979), pp. 61-69.
    • (1979) Trans. Amer. Math. Soc. , vol.251 , pp. 61-69
    • Ioffe, A.D.1
  • 29
    • 0000280429 scopus 로고
    • On subdifferentiability spaces
    • _, On subdifferentiability spaces, Ann. New York Acad. Sci., 410 (1983), pp. 107-119.
    • (1983) Ann. New York Acad. Sci. , vol.410 , pp. 107-119
  • 30
    • 0002665175 scopus 로고
    • Subdifferentiability spaces and nonsmooth analysis
    • _, Subdifferentiability spaces and nonsmooth analysis, Bull. Amer. Math. Soc., 10 (1984), pp. 87-90.
    • (1984) Bull. Amer. Math. Soc. , vol.10 , pp. 87-90
  • 31
    • 0021421971 scopus 로고
    • Necessary conditions for nonsmooth optimization
    • _, Necessary conditions for nonsmooth optimization, Math. Oper. Res., 9 (1984), pp. 159-189.
    • (1984) Math. Oper. Res. , vol.9 , pp. 159-189
  • 32
    • 0001069625 scopus 로고
    • Calculus of Dini subdifferentials of functions and contingent derivatives of set-valued maps
    • _, Calculus of Dini subdifferentials of functions and contingent derivatives of set-valued maps. Nonlinear Anal., 8 (1984), pp. 517-539.
    • (1984) Nonlinear Anal. , vol.8 , pp. 517-539
  • 33
    • 0001413988 scopus 로고
    • On the local surjection property
    • _, On the local surjection property, Nonlinear Anal., 11 (1987), pp. 565-590.
    • (1987) Nonlinear Anal. , vol.11 , pp. 565-590
  • 34
    • 84960582452 scopus 로고
    • Proximal analysis and approximate subdifferentialsm
    • _, Proximal analysis and approximate subdifferentialsm J. London Math. Soc., 41 (1990), pp. 175-192.
    • (1990) J. London Math. Soc. , vol.41 , pp. 175-192
  • 36
    • 0000259921 scopus 로고
    • Extremal points and Euler equations in nonsmooth optimization
    • In Russian
    • A. Y. KRUGER AND B. S. MORDUKHOVICH, Extremal points and Euler equations in nonsmooth optimization, Dokl. Akad. Nauk. BSSR, 24 (1980), pp. 684-687. (In Russian.)
    • (1980) Dokl. Akad. Nauk. BSSR , vol.24 , pp. 684-687
    • Kruger, A.Y.1    Mordukhovich, B.S.2
  • 38
    • 0004186596 scopus 로고
    • Optimal Control via Nonsmooth Analysis
    • Amer. Math. Soc., Summer School on Control, CRM, Université de Montréal, 1992, Amer. Math. Soc., Providence
    • P. D. LOEWEN, Optimal Control via Nonsmooth Analysis, CRM Lecture Notes Series, Amer. Math. Soc., Summer School on Control, CRM, Université de Montréal, 1992, Amer. Math. Soc., Providence, 1993.
    • (1993) CRM Lecture Notes Series
    • Loewen, P.D.1
  • 39
    • 84966250815 scopus 로고
    • Complete characterization of openness, metric regularity, and Lipschitzian properties of multifuntions
    • B. MORDUKHOVICH, Complete characterization of openness, metric regularity, and Lipschitzian properties of multifuntions, Trans. Amer. Math. Soc., 340 (1993), pp. 1-35.
    • (1993) Trans. Amer. Math. Soc. , vol.340 , pp. 1-35
    • Mordukhovich, B.1
  • 40
    • 33646940121 scopus 로고
    • Maximum principle in problems of time optimal control with nonsmooth constraints
    • _, Maximum principle in problems of time optimal control with nonsmooth constraints, J. Appl. Math. Mech., 40 (1976), pp. 960-969.
    • (1976) J. Appl. Math. Mech. , vol.40 , pp. 960-969
  • 41
    • 0000551562 scopus 로고
    • Generalized differential calculus for nonsmooth and set-valued mappings
    • _, Generalized differential calculus for nonsmooth and set-valued mappings, J. Math. Anal. Appl., 183 (1994), pp. 250-288.
    • (1994) J. Math. Anal. Appl. , vol.183 , pp. 250-288
  • 43
    • 0003323056 scopus 로고
    • Convex Functions, Monotone Operators and Differentiability
    • Springer-Verlag, New York, Berlin, Tokyo, 2nd ed., 1993
    • R. R. PHELPS, Convex Functions, Monotone Operators and Differentiability, Lecture Notes in Math. 1364, Springer-Verlag, New York, Berlin, Tokyo, 1988, 2nd ed., 1993.
    • (1988) Lecture Notes in Math. , vol.1364
    • Phelps, R.R.1
  • 44
    • 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
  • 45
    • 0021938097 scopus 로고
    • Extensions of subgradients and its applications to optimization
    • _, Extensions of subgradients and its applications to optimization, Nonlinear Anal., 9 (1985), pp. 665-698.
    • (1985) Nonlinear Anal. , vol.9 , pp. 665-698
  • 46
    • 0002954653 scopus 로고
    • Subdifferentials of compactly Lipschitzian vector valued functions
    • L. THIBAULT, Subdifferentials of compactly Lipschitzian vector valued functions, Ann. Math. Pura Appl. (4), 125 (1980), pp. 157-192.
    • (1980) Ann. Math. Pura Appl. (4) , vol.125 , pp. 157-192
    • Thibault, L.1
  • 47
    • 0023421654 scopus 로고
    • Nonsmooth calculus in finite dimensions
    • D. E. WARD AND J. M. BORWEIN, Nonsmooth calculus in finite dimensions, SIAM J. Control Optim., 25 (1987), pp. 1312-1340.
    • (1987) SIAM J. Control Optim. , vol.25 , pp. 1312-1340
    • Ward, D.E.1    Borwein, J.M.2
  • 48
    • 0003248045 scopus 로고
    • Derivate containers, inverse functions, and controllability
    • D. L. Russell, ed., Academic Press, New York
    • J. WARGA, Derivate containers, inverse functions, and controllability, in Calculus of Variations and Control Theory, D. L. Russell, ed., Academic Press, New York, 1976.
    • (1976) Calculus of Variations and Control Theory
    • Warga, J.1
  • 49
    • 0000169893 scopus 로고
    • Fat homeomorphisms and unbounded derivate containers
    • _, Fat homeomorphisms and unbounded derivate containers, J. Math. Anal. Appl., 81 (1981), pp. 545-560.
    • (1981) J. Math. Anal. Appl. , vol.81 , pp. 545-560


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