메뉴 건너뛰기




Volumn 4, Issue 1, 1996, Pages 1-24

Proximal analysis in smooth spaces

Author keywords

Clarke subdifferentials; Distance functions; G subdifferentials; Lipschitz functions; Lower semi continuous functions; Normals; Smooth renorms; Sub derivatives; Tangent cones; Variational principles

Indexed keywords


EID: 0002425588     PISSN: 09276947     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00419371     Document Type: Article
Times cited : (39)

References (26)
  • 1
    • 0003006591 scopus 로고
    • Minimal cuscos and subgradients of Lipschitz functions
    • J.-B. Baillon and M. Thera (eds), Pitman Lecture Notes in Math., Longman, Harlow
    • Borwein, J. M.: Minimal cuscos and subgradients of Lipschitz functions, in: J.-B. Baillon and M. Thera (eds), Fixed Point Theory and its Applications, Pitman Lecture Notes in Math., Longman, Harlow, 1991, pp. 57-82.
    • (1991) Fixed Point Theory and Its Applications , pp. 57-82
    • Borwein, J.M.1
  • 3
    • 0002830755 scopus 로고    scopus 로고
    • Weak-star sequential compactness and bornological limit derivatives
    • in press
    • Borwein, J. M. and Fitzpatrick, S.: Weak-star sequential compactness and bornological limit derivatives, Convex Analysis, in press.
    • Convex Analysis
    • Borwein, J.M.1    Fitzpatrick, S.2
  • 4
    • 0039037850 scopus 로고
    • Minimal convex uscos and monotone operators on small sets
    • Borwein, J. M., Fitzpatrick, S. and Kenderov, P.: Minimal convex uscos and monotone operators on small sets, Canad. J. Math. 43 (1991), 461-477.
    • (1991) Canad. J. Math. , vol.43 , pp. 461-477
    • Borwein, J.M.1    Fitzpatrick, S.2    Kenderov, P.3
  • 5
    • 84966213239 scopus 로고
    • A smooth variational principle with application to subdifferentiability and differentiability of convex functions
    • Borwein, J. M. and Preiss, D.: A smooth variational principle with application to subdifferentiability and differentiability of convex functions, Trans. Amer. Math. Soc. 303 (1987), 517-527.
    • (1987) Trans. Amer. Math. Soc. , vol.303 , pp. 517-527
    • Borwein, J.M.1    Preiss, D.2
  • 6
    • 0000151286 scopus 로고
    • Proximal analysis and boundaries of closed sets in Banach space, Part I: Theory
    • Borwein, J. M. and Strojwas, H. M.: Proximal analysis and boundaries of closed sets in Banach space, Part I: Theory, Canad. J. Math. 38 (1986), 431-452.
    • (1986) Canad. J. Math. , vol.38 , pp. 431-452
    • Borwein, J.M.1    Strojwas, H.M.2
  • 7
    • 0000778852 scopus 로고
    • Proximal analysis and boundaries of closed sets in Banach space. Part II: Applications
    • Borwein, J. M. and Strojwas, H. M.: Proximal analysis and boundaries of closed sets in Banach space. Part II: Applications, Canad. J. Math. 39 (1987), 428-472.
    • (1987) Canad. J. Math. , vol.39 , pp. 428-472
    • Borwein, J.M.1    Strojwas, H.M.2
  • 12
    • 0004043028 scopus 로고
    • Graduate Texts in Math. Springer-Verlag, New York, Berlin, Tokyo
    • Diestel, J.: Sequences and Series in Banach Spaces, Graduate Texts in Math. Springer-Verlag, New York, Berlin, Tokyo, 1984.
    • (1984) Sequences and Series in Banach Spaces
    • Diestel, J.1
  • 13
    • 0016092731 scopus 로고
    • On the variational principle
    • Ekeland, J.: On the variational principle, J. Math. Anal. Appl. 47 (1974), 324-353.
    • (1974) J. Math. Anal. Appl. , vol.47 , pp. 324-353
    • Ekeland, J.1
  • 15
    • 0001069625 scopus 로고
    • Calculus of Dini subdifferentials of functions and contingent derivatives of set-valued maps
    • Ioffe, A.: Calculus of Dini subdifferentials of functions and contingent derivatives of set-valued maps, Nonlinear Anal. 8 (1984), 517-539.
    • (1984) Nonlinear Anal. , vol.8 , pp. 517-539
    • Ioffe, A.1
  • 16
    • 84966259071 scopus 로고
    • Approximate subdifferentials and applications 3. the metric theory
    • Ioffe, A.: Approximate subdifferentials and applications 3. The metric theory, Mathematika 36 (1989), 1-38.
    • (1989) Mathematika , vol.36 , pp. 1-38
    • Ioffe, A.1
  • 17
    • 84960582452 scopus 로고
    • Proximal analysis and approximate subdifferentials
    • Ioffe, A.: Proximal analysis and approximate subdifferentials, J. London Math. Soc. 41 (1990), 175-192.
    • (1990) J. London Math. Soc. , vol.41 , pp. 175-192
    • Ioffe, A.1
  • 18
    • 0010808263 scopus 로고
    • Generalized differentials of nonsmooth functions and necessary conditions for an extremum
    • Kruger, A.: Generalized differentials of nonsmooth functions and necessary conditions for an extremum, Siberian J. Math. 26 (1985), 370-379.
    • (1985) Siberian J. Math. , vol.26 , pp. 370-379
    • Kruger, A.1
  • 19
    • 0000259921 scopus 로고
    • Extremal points and Euler equation in nonsmooth optimization
    • in Russian
    • Kruger, A. and Mordukhovich, B.: Extremal points and Euler equation in nonsmooth optimization, Dokl. Akad. Nauk BSSR 24 (1980), 684-687 (in Russian).
    • (1980) Dokl. Akad. Nauk BSSR , vol.24 , pp. 684-687
    • Kruger, A.1    Mordukhovich, B.2
  • 20
    • 0039561243 scopus 로고
    • Gateaux differentiability of convex functions on Banach spaces
    • Larman, D. and Phelps, R. R.: Gateaux differentiability of convex functions on Banach spaces, J. London. Math. Soc. 20 (1979), 115-127.
    • (1979) J. London. Math. Soc. , vol.20 , pp. 115-127
    • Larman, D.1    Phelps, R.R.2
  • 21
    • 0001442538 scopus 로고
    • Limits of Fréchet normals in nonsmooth analysis
    • A. Ioffe, M. Marcus, and S. Reich (eds), Longman, Harlow
    • Loewen, P. D.: Limits of Fréchet normals in nonsmooth analysis, in: A. Ioffe, M. Marcus, and S. Reich (eds), Optimization and Nonlinear Analysis, Longman, Harlow, 1992, pp. 178-188.
    • (1992) Optimization and Nonlinear Analysis , pp. 178-188
    • Loewen, P.D.1
  • 25
    • 0000107568 scopus 로고
    • Fréchet derivatives of Lipschitzian functions
    • Preiss, D.: Fréchet derivatives of Lipschitzian functions, J. Funct. Anal. 91 (1990), 312-345.
    • (1990) J. Funct. Anal. , vol.91 , pp. 312-345
    • Preiss, D.1
  • 26
    • 84967712868 scopus 로고
    • Clarke's gradients and epsilon-subgradients in Banach spaces
    • Treiman, J. S.: Clarke's gradients and epsilon-subgradients in Banach spaces, Trans. Amer. Math. Soc. 294 (1986), 65-78.
    • (1986) Trans. Amer. Math. Soc. , vol.294 , pp. 65-78
    • Treiman, J.S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.