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Volumn 12, Issue 1-2, 2004, Pages 25-47

Prox-regularity of functions and sets in Banach spaces

Author keywords

Convex function; Convexly composite function; Moreau envelope; Prox regular function; Subdifferential

Indexed keywords


EID: 3943109539     PISSN: 09276947     EISSN: None     Source Type: Journal    
DOI: 10.1023/b:svan.0000023403.87092.a2     Document Type: Article
Times cited : (51)

References (33)
  • 4
    • 79951822899 scopus 로고
    • The proximal normal formula in Banach space
    • Borwein, J. M. and Giles, J. R.: The proximal normal formula in Banach space, Trans. Amer. Math. Soc. 302 (1987), 371-381.
    • (1987) Trans. Amer. Math. Soc. , vol.302 , pp. 371-381
    • Borwein, J.M.1    Giles, J.R.2
  • 9
    • 0033441597 scopus 로고    scopus 로고
    • Convergence of subdifferentials of convexly composite functions
    • Combari, C., Poliquin, R. A. and Thibault, L.: Convergence of subdifferentials of convexly composite functions, Canad. J. Math. 51 (1999), 250-265.
    • (1999) Canad. J. Math. , vol.51 , pp. 250-265
    • Combari, C.1    Poliquin, R.A.2    Thibault, L.3
  • 10
    • 0242595928 scopus 로고    scopus 로고
    • Epi-convergence of convexly composite functions in Banach spaces
    • to appear
    • Combari, C. and Thibault, L.: Epi-convergence of convexly composite functions in Banach spaces, SIAM J. Optim., to appear.
    • SIAM J. Optim.
    • Combari, C.1    Thibault, L.2
  • 11
    • 84966220672 scopus 로고
    • Characterization of lower semicontinuous convex functions
    • Correa, R., Jofré, A. and Thibault, L.: Characterization of lower semicontinuous convex functions, Proc. Amer. Math. Soc. 116 (1992), 61-72.
    • (1992) Proc. Amer. Math. Soc. , vol.116 , pp. 61-72
    • Correa, R.1    Jofré, A.2    Thibault, L.3
  • 12
    • 0001672299 scopus 로고
    • Subdifferential monotonicity as characterization of convex functions
    • Correa, R., Jofré, A. and Thibault, L.: Subdifferential monotonicity as characterization of convex functions, Numer. Funct. Anal. Optim. 15 (1994), 531-536.
    • (1994) Numer Funct. Anal. Optim. , vol.15 , pp. 531-536
    • Correa, R.1    Jofré, A.2    Thibault, L.3
  • 15
    • 84966198944 scopus 로고
    • Nonconvex minimization problems
    • Ekeland, I.: Nonconvex minimization problems, Bull. Amer. Math. Soc. 1 (1979), 443-474.
    • (1979) Bull. Amer. Math. Soc. , vol.1 , pp. 443-474
    • Ekeland, I.1
  • 16
    • 0001733553 scopus 로고
    • On the number of periodic trajectories for a Hamiltonian flow
    • Ekeland, I. and Lasry, J.-M.: On the number of periodic trajectories for a Hamiltonian flow, Ann. of Math. 112 (1980), 293-319.
    • (1980) Ann. of Math. , vol.112 , pp. 293-319
    • Ekeland, I.1    Lasry, J.-M.2
  • 17
    • 84960582452 scopus 로고
    • Proximal analysis and approximate subdifferentials
    • Ioffe, A. D.: 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
  • 18
    • 3943052967 scopus 로고    scopus 로고
    • On primal lower nice property
    • Ivanov, M. and Zlateva, N.: On primal lower nice property, C.R. Acad. Bulgare Sci. 54(11) (2001), 5-10.
    • (2001) C.R. Acad. Bulgare Sci. , vol.54 , Issue.11 , pp. 5-10
    • Ivanov, M.1    Zlateva, N.2
  • 20
    • 84966232303 scopus 로고
    • Partial extension of Attouch's theorem with applications to proto-derivatives of subgradient mappings
    • Levy, A. B., Poliquin, R. A. and Thibault, L.: Partial extension of Attouch's theorem with applications to proto-derivatives of subgradient mappings, Trans. Amer. Math. Soc. 347 (1995), 1269-1294.
    • (1995) Trans. Amer. Math. Soc. , vol.347 , pp. 1269-1294
    • Levy, A.B.1    Poliquin, R.A.2    Thibault, L.3
  • 21
    • 84972527138 scopus 로고
    • A generalized derivative for calm and stable functions
    • Michel, Ph. and Penot, J.-P.: A generalized derivative for calm and stable functions, Differential Integral Equations 5 (1992), 433-454.
    • (1992) Differential Integral Equations , vol.5 , pp. 433-454
    • Michel, Ph.1    Penot, J.-P.2
  • 22
    • 0001254208 scopus 로고
    • Metric approximation and necessary optimality conditions for general classes of nonsmooth extremal problems
    • Mordukhovich, B. S.: Metric approximation 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
  • 23
    • 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. 124 (1996), 1235-1280.
    • (1996) Trans. Amer. Math. Soc. , vol.124 , pp. 1235-1280
    • Mordukhovich, B.S.1    Shao, Y.2
  • 24
    • 0000276924 scopus 로고
    • Proximité et dualité dans un espace hilbertien
    • Moreau, J.-J.: Proximité et dualité dans un espace hilbertien, Bull. Soc. Math. France 93 (1965), 273-299.
    • (1965) Bull. Soc. Math. France , vol.93 , pp. 273-299
    • Moreau, J.-J.1
  • 25
    • 0024050952 scopus 로고
    • Approximation and decomposition properties of some classes of locally d.c. functions
    • Penot, J.-P. and Bougeard, M.: Approximation and decomposition properties of some classes of locally d.c. functions, Math. Programming 41 (1988), 195-227.
    • (1988) Math. Programming , vol.41 , pp. 195-227
    • Penot, J.-P.1    Bougeard, M.2
  • 26
    • 0000304890 scopus 로고
    • Integration of subdifferentials of nonconvex functions
    • Poliquin, R. A.: Integration of subdifferentials of nonconvex functions, Nonlinear Anal. Th. Meth. Appl. 17 (1991), 385-398.
    • (1991) Nonlinear Anal. Th. Meth. Appl. , vol.17 , pp. 385-398
    • Poliquin, R.A.1
  • 27
    • 0007633319 scopus 로고    scopus 로고
    • Prox-regular functions in variational analysis
    • Poliquin, R. A. and Rockafellar, R. T.: Prox-regular functions in variational analysis, Trans. Amer. Math. Soc. 348 (1996), 1805-1838.
    • (1996) Trans. Amer. Math. Soc. , vol.348 , pp. 1805-1838
    • Poliquin, R.A.1    Rockafellar, R.T.2
  • 29
    • 84966228167 scopus 로고
    • First and second order epi-differentiability in nonlinear programming
    • Rockafellar, R. T.: First and second order epi-differentiability in nonlinear programming, Trans. Amer. Math. Soc. 307 (1988), 75-107.
    • (1988) Trans. Amer. Math. Soc. , vol.307 , pp. 75-107
    • Rockafellar, R.T.1
  • 31
    • 0001477709 scopus 로고
    • A note on the Zagrodny mean value theorem
    • Thibault, L.: A note on the Zagrodny mean value theorem, Optimization 35 (1995), 127-130.
    • (1995) Optimization , vol.35 , pp. 127-130
    • Thibault, L.1
  • 32
    • 0003030229 scopus 로고
    • Integration of subdifferentials of lower semicontinuous functions on Banach spaces
    • Thibault, L. and Zagrodny, D.: Integration of subdifferentials of lower semicontinuous functions on Banach spaces, J. Math. Anal. Appl. 189 (1995), 33-58.
    • (1995) J. Math. Anal. Appl. , vol.189 , pp. 33-58
    • Thibault, L.1    Zagrodny, D.2
  • 33
    • 50749132985 scopus 로고
    • Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces
    • Xu, Z.-B. and Roach, G. F.: Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces, J. Math. Anal. Appl. 157 (1991), 189-210.
    • (1991) J. Math. Anal. Appl. , vol.157 , pp. 189-210
    • Xu, Z.-B.1    Roach, G.F.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.