메뉴 건너뛰기




Volumn 189, Issue 1, 1995, Pages 33-58

Integration of Subdifferentials of Lower Semicontinuous Functions on Banach Spaces

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0003030229     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1006/jmaa.1995.1003     Document Type: Article
Times cited : (103)

References (33)
  • 2
    • 84966213239 scopus 로고
    • A smooth variational principle with applications to subdifferentiability and to differentiability of convex functions
    • J. M. Borwein and D. Prfiss, A smooth variational principle with applications to subdifferentiability and to differentiability of convex functions. Trims. Amer. Math. Soc. 303 (1987), 517-527.
    • (1987) Trims. Amer. Math. Soc , vol.303 , pp. 517-527
    • Borwein, J.M.1    Prfiss, D.2
  • 3
    • 79951822899 scopus 로고
    • The proximal normal formula in Banach space
    • J. M. Borwfin and J. R. Giles, The proximal normal formula in Banach space, Trims. Amer. Math. Soc. 302 (1987), 371-381.
    • (1987) Trims. Amer. Math. Soc , vol.302 , pp. 371-381
    • Borwfin, J.M.1    Giles, J.R.2
  • 5
    • 0002348314 scopus 로고
    • Tangentially continuous directional derivatives in nonsmooth analysis
    • R. Correa and A. Jofre, Tangentially continuous directional derivatives in nonsmooth analysis, J. Optim. Theory Appl. 61 (1989), 1-21.
    • (1989) J. Optim. Theory Appl , vol.61 , pp. 1-21
    • Correa, R.1    Jofre, A.2
  • 6
    • 84966220672 scopus 로고
    • Characterization of lower semi-continuous convex functions
    • R. Correa, A. Jofre, and L. Thibault, Characterization of lower semi-continuous convex functions, Proc. Amer. Soc. 116 (1992), 61-72.
    • (1992) Proc. Amer. Soc , vol.116 , pp. 61-72
    • Correa, R.1    Jofre, A.2    Thibault, L.3
  • 7
    • 0001672299 scopus 로고
    • Subdifferential monotonicity as characterization of convex functions
    • R. Correa, A. Jofre, and L. Thibault, Subdifferential monotonicity as characterization of convex functions, Nitmer. Fund. Anal. Optiiniz. 15 (1994), 531-536.
    • (1994) Nitmer. Fund. Anal. Optiiniz , vol.15 , pp. 531-536
    • Correa, R.1    Jofre, A.2    Thibault, L.3
  • 8
    • 38249016393 scopus 로고
    • Subdifferential analysis of bivariate separate regular functions
    • R. Correa and L. Thibault, Subdifferential analysis of bivariate separate regular functions, J. Mailt. Anal. Appl. 148(1990), 157-174.
    • (1990) J. Mailt. Anal. Appl , vol.148 , pp. 157-174
    • Correa, R.1    Thibault, L.2
  • 10
    • 0039004011 scopus 로고
    • A note on the mean value theorem for convex functions
    • J.-B. Hiriart-Urruty, A note on the mean value theorem for convex functions, Boll. Un. Mat. Ital. B 17 (1980). 765-775.
    • (1980) Boll. Un. Mat. Ital. B , vol.17 , pp. 765-775
    • Hiriart-Urruty, J.-B.1
  • 11
    • 84974312624 scopus 로고
    • Approximate subdifferentials and applications, 2 and 3
    • A. D. Ioffe, Approximate subdifferentials and applications, 2 and 3, Mathemalika 33 (1986), 111-128;
    • (1986) Mathemalika , vol.33 , pp. 111-128
    • Ioffe, A.D.1
  • 12
    • 84966259071 scopus 로고
    • Approximate subdifferentials and applications, 2 and 3
    • A. D. Ioffe, Approximate subdifferentials and applications, 2 and 3, Mathemalika 36 (1989), 1-36.
    • (1989) Mathemalika , vol.36 , pp. 1-36
    • Ioffe, A.D.1
  • 13
    • 84960582452 scopus 로고
    • Proximal analysis and approximate subdifferentials
    • A. D. Ioffe, 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.D.1
  • 14
    • 84966234231 scopus 로고
    • D-representation of subdifferentials of directionally Lipschitz functions
    • A. Jofre and L. Thibault, D-representation of subdifferentials of directionally Lipschitz functions, Proc. Amer. Math. Soc. 110 (1990), 117-123.
    • (1990) Proc. Amer. Math. Soc , vol.110 , pp. 117-123
    • Jofre, A.1    Thibault, L.2
  • 15
    • 44049109741 scopus 로고
    • Proximal and Frechet normal formulae for some small normal cones in Hilbert spaces
    • A. Jofre and L. Thibault, Proximal and Frechet normal formulae for some small normal cones in Hilbert spaces, Nonlinear Anal. Theory Meth. Appl. 19(1992), 599-612.
    • (1992) Nonlinear Anal. Theory Meth. Appl , vol.19 , pp. 599-612
    • Jofre, A.1    Thibault, L.2
  • 16
    • 0001472337 scopus 로고
    • Properties of generalized differentials
    • A. Y. Kruger, Properties of generalized differentials, Siberian Math. J. (1983), 822-832.
    • (1983) Siberian Math. J , pp. 822-832
    • Kruger, A.Y.1
  • 17
    • 0000259921 scopus 로고
    • Extreme points and the Euler in nondifferentiable optimization problems
    • A. Y. Kruger and Mordukhovich, M. Extreme points and the Euler in nondifferentiable optimization problems, Dokl. Akad. Nauk BSSR 24 (1982), 684-687.
    • (1982) Dokl. Akad. Nauk BSSR , vol.24 , pp. 684-687
    • Kruger, A.Y.1    Mordukhovich, M.2
  • 18
    • 3042918829 scopus 로고
    • An application of Ekeland’s theorem to minimax problems
    • L. McLinden, An application of Ekeland’s theorem to minimax problems. Nonlinear Anal. Theory Meth. Appl. 6 (1982), 189-196.
    • (1982) Nonlinear Anal. Theory Meth. Appl , vol.6 , pp. 189-196
    • McLinden, L.1
  • 19
    • 84972527138 scopus 로고
    • A generalized derivative for calm and stable functions
    • Ph. Michel and M. Penot, A generalized derivative for calm and stable functions, Differential integral Equations 5 (1992), 189-196.
    • (1992) Differential Integral Equations , vol.5 , pp. 189-196
    • Michel, P.H.1    Penot, M.2
  • 20
    • 0001254208 scopus 로고
    • Metric approximations and necessary optimality conditions for general classes of nonsmooth extremal problems
    • B. S. Mordukhovich, Metric approximations and necessary optimality conditions for general classes of nonsmooth extremal problems, Soviet Math. Dokl. 22 (1980), 526-530.
    • (1980) Soviet Math. Dokl , vol.22 , pp. 526-530
    • Mordukhovich, B.S.1
  • 22
    • 0006419629 scopus 로고
    • Subgradient monotonicity and convex functions
    • R. A. Poliquin, Subgradient monotonicity and convex functions, Nonlinear Anal. Theory Meth. Appl. 14 (1990), 305-317.
    • (1990) Nonlinear Anal. Theory Meth. Appl , vol.14 , pp. 305-317
    • Poliquin, R.A.1
  • 23
    • 0000304890 scopus 로고
    • Integration of subdifferentials of nonconvex functions
    • R. A. Poliquin, Integration of subdifferentials of nonconvex functions, Nonlinear Anal. Theory’ Meth. Appl. 17 (1991), 385-398.
    • (1991) Nonlinear Anal. Theory’ Meth. Appl , vol.17 , pp. 385-398
    • Poliquin, R.A.1
  • 24
    • 38249004911 scopus 로고
    • The maximal normal operator space and integration of subdifferentials of nonconvex functions
    • L. Qi, The maximal normal operator space and integration of subdifferentials of nonconvex functions. Nonlinear Anal. Theory Meth. Appl. 13 (1989), 1003-1012.
    • (1989) Nonlinear Anal. Theory Meth. Appl , vol.13 , pp. 1003-1012
    • Qi, L.1
  • 25
    • 0016993914 scopus 로고
    • Stability theory for systems of inequalities in nonlinear programming, II. Differentiable nonlinear systems
    • S. M. Robinson, Stability theory for systems of inequalities in nonlinear programming, II. Differentiable nonlinear systems, SIAM J. Numer. Anal. 13 (1976), 497-513.
    • (1976) SIAM J. Numer. Anal , vol.13 , pp. 497-513
    • Robinson, S.M.1
  • 26
    • 0004267646 scopus 로고
    • Princeton Univ. Press, Princeton, NJ
    • R. T. Rockafellar. "Convex Analysis," Princeton Univ. Press, Princeton, NJ, 1970.
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 27
    • 84972545670 scopus 로고
    • Characterization of the subdifferentials of convex functions
    • R. T. Rockafellar, Characterization of the subdifferentials of convex functions. Pacific J. Math. 17 (1966), 497-510.
    • (1966) Pacific J. Math , vol.17 , pp. 497-510
    • Rockafellar, R.T.1
  • 28
    • 84972582929 scopus 로고
    • On the maximal monotonicity of subdifferential mappings
    • R. T. Rockafellar, On the maximal monotonicity of subdifferential mappings, Pacific J. Math. 33 (1970), 209-216.
    • (1970) Pacific J. Math , vol.33 , pp. 209-216
    • Rockafellar, R.T.1
  • 29
    • 0002085846 scopus 로고
    • Favorable classes of Lipschitz-continuous functions in subgradient optimization
    • E. Nurminski, Ed, IIASA Collaborative Proceedings Series, International Institute of Applied Systems Analysis, Laxenburg, Austria
    • R. T. Rockafellar, Favorable classes of Lipschitz-continuous functions in subgradient optimization, in “Progress in Nondifferentiable Optimization” (E. Nurminski, Ed.), pp. 125-144, IIASA Collaborative Proceedings Series, International Institute of Applied Systems Analysis, Laxenburg, Austria, 1982.
    • (1982) Progress in Nondifferentiable Optimization , pp. 125-144
    • Rockafellar, R.T.1
  • 30
    • 0000295695 scopus 로고
    • Generalized directional derivatives and subgradients of nonconvex functions
    • R. T. Rockafellar, Generalized directional derivatives and subgradients of nonconvex functions, Canad. J. Math. 32 (1980), 257-280.
    • (1980) Canad. J. Math , vol.32 , pp. 257-280
    • Rockafellar, R.T.1
  • 32
    • 0001161272 scopus 로고
    • Approximate mean value theorem for upper subderivatives
    • D. Zagrodny, Approximate mean value theorem for upper subderivatives. Nonlinear Anal. Theory Meth. Appl. 12 (1988), 1413-1428.
    • (1988) Nonlinear Anal. Theory Meth. Appl , vol.12 , pp. 1413-1428
    • Zagrodny, D.1
  • 33
    • 0002800189 scopus 로고
    • Regularity and stability for mathematical programming problems in Banach space
    • J. Zowr. and S. Kurcyusz, Regularity and stability for mathematical programming problems in Banach space, Appl. Math. Optim. 5 (1979), 49-62.
    • (1979) Appl. Math. Optim , vol.5 , pp. 49-62
    • Zowr, J.1    Kurcyusz, S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.