메뉴 건너뛰기




Volumn 9, Issue 1-2, 2001, Pages 187-216

Metric Inequality, Subdifferential Calculus and Applications

Author keywords

Asplund space; Composite function; Limiting fr chet subdifferential; Metric inequality; Normal cone; Optimality condtion; Painlev Kuratowski convergence

Indexed keywords


EID: 0042283592     PISSN: 09276947     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1011291608129     Document Type: Article
Times cited : (70)

References (38)
  • 1
    • 22044439655 scopus 로고    scopus 로고
    • Nescessary conditions for constrained optimization problems with semicontinuous and continuous data
    • Borwein, J. M., Treiman, J. S. and Zhu, Q. S.: Nescessary conditions for constrained optimization problems with semicontinuous and continuous data, Trans. Amer. Math. Soc. 350 (1998), 2409-2429.
    • (1998) Trans. Amer. Math. Soc. , vol.350 , pp. 2409-2429
    • Borwein, J.M.1    Treiman, J.S.2    Zhu, Q.S.3
  • 5
    • 0016092731 scopus 로고
    • On the variational principle
    • Ekeland, I.: On the variational principle, J. Math. Anal. Appl. 47 (1970), 324-353.
    • (1970) J. Math. Anal. Appl. , vol.47 , pp. 324-353
    • Ekeland, I.1
  • 6
    • 84962984436 scopus 로고
    • Subdifferentials, local ∈-supports and Asplund spaces
    • Fabian, M.: Subdifferentials, local ∈-supports and Asplund spaces, J. London Math. Soc. 34 (1986), 569-576.
    • (1986) J. London Math. Soc. , vol.34 , pp. 569-576
    • Fabian, M.1
  • 7
    • 0002574218 scopus 로고
    • Subdifferentiability and trustworthiness in the light of a new variational principle of Borwein and Preiss
    • Fabian, M.: Subdifferentiability and trustworthiness in the light of a new variational principle of Borwein and Preiss, Acta Univ. Carolinae 30 (1989), 51-56.
    • (1989) Acta Univ. Carolinae , vol.30 , pp. 51-56
    • Fabian, M.1
  • 8
    • 0001342523 scopus 로고    scopus 로고
    • Nonsmooth characterizations of Asplund spaces and smooth variational principles
    • Fabian, M. and Mordukhovich, B. S.: Nonsmooth characterizations of Asplund spaces and smooth variational principles, Set-Valued Anal. 6 (1998), 381-406.
    • (1998) Set-Valued Anal. , vol.6 , pp. 381-406
    • Fabian, M.1    Mordukhovich, B.S.2
  • 10
    • 84966259071 scopus 로고
    • Approximate subdifferential and applications, Part 3
    • Ioffe, A. D.: Approximate subdifferential and applications, Part 3, Mathematika 36 (1989), 1-38.
    • (1989) Mathematika , vol.36 , pp. 1-38
    • Ioffe, A.D.1
  • 11
    • 84960582452 scopus 로고
    • Proximal analysis and approximate subdifferential
    • Ioffe, A. D.: Proximal analysis and approximate subdifferential, J. London Math. Soc. 41 (1990).
    • (1990) J. London Math. Soc. , vol.41
    • Ioffe, A.D.1
  • 12
    • 0001264936 scopus 로고    scopus 로고
    • Codirectional compactness, metric regularity and subdifferential calculus
    • Michel Théra (ed.), Experimental, Constructive and Nonlinear Analysis
    • Ioffe, A.: Codirectional compactness, metric regularity and subdifferential calculus, In: Michel Théra (ed.), Experimental, Constructive and Nonlinear Analysis, Canadian Math. Soc. Proc. Serie 27, 2000, pp. 123-163.
    • (2000) Canadian Math. Soc. Proc. Serie , vol.27 , pp. 123-163
    • Ioffe, A.1
  • 13
    • 0032119584 scopus 로고    scopus 로고
    • ∈-subdifferential and ∈-monotonicity
    • Jofré, A., Luc, D. T., Théra, M.: ∈-subdifferential and ∈-monotonicity, Nonlinear Anal. 33 (1998), 71-90.
    • (1998) Nonlinear Anal. , vol.33 , pp. 71-90
    • Jofré, A.1    Luc, D.T.2    Théra, M.3
  • 14
    • 0038328485 scopus 로고
    • Intersection formulae and the marginal function in Banach spaces
    • Jourani, A.: Intersection formulae and the marginal function in Banach spaces, J. Math. Anal. Appl. 192 (1995), 867-891.
    • (1995) J. Math. Anal. Appl. , vol.192 , pp. 867-891
    • Jourani, A.1
  • 15
    • 0038667088 scopus 로고    scopus 로고
    • The role of locally compact cones in nonsmooth analysis
    • Jourani, A.: The role of locally compact cones in nonsmooth analysis, Comm. Appl. Nonlinear Anal. 5 (1998), 1-35.
    • (1998) Comm. Appl. Nonlinear Anal. , vol.5 , pp. 1-35
    • Jourani, A.1
  • 16
    • 85017212795 scopus 로고    scopus 로고
    • On limiting Fréchet ∈-subdifferentials
    • J. P. Crouzeix et al. (eds), Kluwer Acad. Publ., Dordrecht
    • Jourani, A. and Théra, M.: On limiting Fréchet ∈-subdifferentials, In: J. P. Crouzeix et al. (eds), Generalized Convexity, Kluwer Acad. Publ., Dordrecht, 1997, pp. 185-198.
    • (1997) Generalized Convexity , pp. 185-198
    • Jourani, A.1    Théra, M.2
  • 17
    • 0033102269 scopus 로고    scopus 로고
    • Coderivatives of multivalued mapping, locally compact cones and metric regularity
    • Jourani, A. and Thibault, L.: Coderivatives of multivalued mapping, locally compact cones and metric regularity, Nonlinear Anal 35 (1999), 925-945.
    • (1999) Nonlinear Anal , vol.35 , pp. 925-945
    • Jourani, A.1    Thibault, L.2
  • 18
    • 0030496625 scopus 로고    scopus 로고
    • Extensions of subdifferential caculus in Banach spaces
    • Jourani, A. and Thibault, L.: Extensions of subdifferential caculus in Banach spaces, Canad. J. Math. 48 (1996), 834-848.
    • (1996) Canad. J. Math. , vol.48 , pp. 834-848
    • Jourani, A.1    Thibault, L.2
  • 19
    • 0010122267 scopus 로고
    • Metric inequality and subdifferential calculus in Banach spaces
    • Jourani, A. and Thibault, L.: Metric inequality and subdifferential calculus in Banach spaces, Set-Valued Anal. 3 (1995), 87-100.
    • (1995) Set-Valued Anal. , vol.3 , pp. 87-100
    • Jourani, A.1    Thibault, L.2
  • 20
    • 22044439768 scopus 로고    scopus 로고
    • Chain rules of coderivatives of multivalued mappings in Banach spaces
    • Jourani, A. and Thibault, L.: Chain rules of coderivatives of multivalued mappings in Banach spaces, Proc. Amer. Math. Soc. 126 (1998), 1479-1486.
    • (1998) Proc. Amer. Math. Soc. , vol.126 , pp. 1479-1486
    • Jourani, A.1    Thibault, L.2
  • 21
    • 0000259921 scopus 로고
    • Extremal points and the Euler equation in nonsmooth optimization
    • Kruger, A. Y. and Mordukhovich, B. S.: Extremal points and the Euler equation in nonsmooth optimization, DAN Akad. Nauk BSSR 24 (1980), 684-687.
    • (1980) DAN Akad. Nauk BSSR , vol.24 , pp. 684-687
    • Kruger, A.Y.1    Mordukhovich, B.S.2
  • 22
    • 0001472337 scopus 로고
    • Properties of generalized subdifferentials
    • Kruger, A. Y.: Properties of generalized subdifferentials, Siberian Math. J. 26 (1985), 822-832.
    • (1985) Siberian Math. J. , vol.26 , pp. 822-832
    • Kruger, A.Y.1
  • 23
    • 0001442538 scopus 로고
    • Limits of Fréchet normals in nonsmooth analysis
    • A. Ioffe et al. (eds), Pitman, London
    • Loewen, P. D.: Limits of Fréchet normals in nonsmooth analysis, In: A. Ioffe et al. (eds), Pitman Res. Notes Math. Ser. 224, Pitman, London, 1992, pp. 178-188.
    • (1992) Pitman Res. Notes Math. Ser. , vol.224 , pp. 178-188
    • Loewen, P.D.1
  • 24
    • 0041945021 scopus 로고    scopus 로고
    • On ∈-convexity and ∈-monotonicity
    • A. Ioffe, S. Reich and I. Shafrir (eds), Chapman & Hall, London
    • Luc, D. T., Ngai, H. and Théra, M.: On ∈-convexity and ∈-monotonicity, In: A. Ioffe, S. Reich and I. Shafrir (eds), Calculus of Variations and Differential Equations, Chapman & Hall, London, 1999, pp. 82-100.
    • (1999) Calculus of Variations and Differential Equations , pp. 82-100
    • Luc, D.T.1    Ngai, H.2    Théra, M.3
  • 25
    • 33646940121 scopus 로고
    • Maximum principle in problems of time optimal control with nonsmooth constraints
    • Mordukhovich, B. S.: Maximum principle in problems of time optimal control with nonsmooth constraints, Appl. Math. Mech. 40 (1976), 960-969.
    • (1976) Appl. Math. Mech. , vol.40 , pp. 960-969
    • Mordukhovich, B.S.1
  • 26
    • 0001254208 scopus 로고
    • Metric approximations and necessary optimality conditions for general class of nonsmooth extremal problems
    • Mordukhovich, B. S.: Metric approximations and necessary optimality conditions for general class of nonsmooth extremal problems, Soviet Math. Dokl. 22 (1980), 526-530.
    • (1980) Soviet Math. Dokl. , vol.22 , pp. 526-530
    • Mordukhovich, B.S.1
  • 28
    • 0001657279 scopus 로고    scopus 로고
    • Extremal characterization of Asplund spaces
    • Mordukhovich, B. S. and Shao, Y.: Extremal characterization of Asplund spaces, Proc. Amer. Math. Soc. 348 (1996), 197-205.
    • (1996) Proc. Amer. Math. Soc. , vol.348 , pp. 197-205
    • Mordukhovich, B.S.1    Shao, Y.2
  • 29
    • 27244452009 scopus 로고    scopus 로고
    • Nonsmooth sequential analysis in Asplund spaces
    • Mordukhovich, B. S. and Shao, Y.: Nonsmooth sequential analysis in Asplund spaces, Trans. Amer. Math. Soc. 348 (1996), 1235-1280.
    • (1996) Trans. Amer. Math. Soc. , vol.348 , pp. 1235-1280
    • Mordukhovich, B.S.1    Shao, Y.2
  • 30
    • 0000644733 scopus 로고
    • On nonconvex subdifferential calculus in Banach spaces
    • Mordukhovich, B. S. and Shao, Y.: On nonconvex subdifferential calculus in Banach spaces, J. Convex Anal. 2 (1995), 211-228.
    • (1995) J. Convex Anal. , vol.2 , pp. 211-228
    • Mordukhovich, B.S.1    Shao, Y.2
  • 32
    • 0010939715 scopus 로고    scopus 로고
    • On variational characterizations of Asplund spaces
    • Michel Théra (ed.), Experimental, Constructive and Nonlinear Analysis
    • Mordukhovich, B. S. and Wang, B.: On variational characterizations of Asplund spaces, In: Michel Théra (ed.), Experimental, Constructive and Nonlinear Analysis, Canadian Math. Soc. Proc. Serie 27, 2000, pp. 245-254.
    • (2000) Canadian Math. Soc. Proc. Serie , vol.27 , pp. 245-254
    • Mordukhovich, B.S.1    Wang, B.2
  • 33
    • 0042445776 scopus 로고    scopus 로고
    • Extensions of Fréchet ∈-subdifferential calculus and application
    • Ngai, H., Luc, D.T. and Théra, M.: Extensions of Fréchet ∈-subdifferential calculus and application, to appear in J. Math. Anal. Appl.
    • J. Math. Anal. Appl.
    • Ngai, H.1    Luc, D.T.2    Théra, M.3
  • 34
    • 0003323056 scopus 로고
    • Convex Functions, Monotone Operator and Differentiability
    • 2nd edn, Springer-Verlag, Berlin
    • Phelps, R. R.: Convex Functions, Monotone Operator and Differentiability (2nd edn), Lecture Notes in Math. 1364, Springer-Verlag, Berlin, 1993.
    • (1993) Lecture Notes in Math. , vol.1364
    • Phelps, R.R.1
  • 35
    • 0000752102 scopus 로고
    • Proximal subgradients, marginal values and augmented Lagrangians in nonconvex optimization
    • Rockafellar, R. T.: Proximal subgradients, marginal values and augmented Lagrangians in nonconvex optimization, Math. Oper. Res. 6 (1981), 424-436.
    • (1981) Math. Oper. Res. , vol.6 , pp. 424-436
    • Rockafellar, R.T.1
  • 36
    • 0026222116 scopus 로고
    • On subdifferentieal of optimal valued function
    • Thibault, L.: On subdifferentieal of optimal valued function, SIAM J. Optim. 29 (1991), 1019-1036.
    • (1991) SIAM J. Optim. , vol.29 , pp. 1019-1036
    • Thibault, L.1
  • 37
    • 0000205969 scopus 로고
    • The linear nonconvex generalized gradient and Lagrange multipliers
    • Treiman, J. S.: The linear nonconvex generalized gradient and Lagrange multipliers, SIAM J. Optim. 5 (1995), 670-679.
    • (1995) SIAM J. Optim. , vol.5 , pp. 670-679
    • Treiman, J.S.1
  • 38
    • 0023421654 scopus 로고
    • Nonconvex calculus in finite dimensions
    • Ward, D. and Borwein, J. M.: Nonconvex calculus in finite dimensions, SIAM J. Control Optim. 25 (1987), 1312-1340.
    • (1987) SIAM J. Control Optim. , vol.25 , pp. 1312-1340
    • Ward, D.1    Borwein, J.M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.