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Volumn 221, Issue 1, 1998, Pages 33-58

Subtraction Theorems and Approximate Openness for Multifunctions: Topological and Infinitesimal Viewpoints

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EID: 0008327558     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1995.5054     Document Type: Article
Times cited : (11)

References (61)
  • 3
    • 85016656725 scopus 로고
    • Convergence of convex-concave saddle functions: Applications to convex programming and mechanics
    • Attouch H., Azé D., Wets R. J. B. Convergence of convex-concave saddle functions: Applications to convex programming and mechanics. Ann. Inst. H. Poincaré Anal. Non Linéaire. 5:1988;537-572.
    • (1988) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.5 , pp. 537-572
    • Attouch, H.1    Azé, D.2    Wets, R.J.B.3
  • 4
    • 0021375867 scopus 로고
    • Lipschitz behavior of solutions to convex optimization problems
    • Aubin J.-P. Lipschitz behavior of solutions to convex optimization problems. Math. Oper. Res. 9:1984;87-111.
    • (1984) Math. Oper. Res. , vol.9 , pp. 87-111
    • Aubin, J.-P.1
  • 7
    • 0010962502 scopus 로고
    • On inverse function theorems for set-valued maps
    • Aubin J.-P., Frankowska H. On inverse function theorems for set-valued maps. J. Math. Pures Appl. 66:1987;71-89.
    • (1987) J. Math. Pures Appl. , vol.66 , pp. 71-89
    • Aubin, J.-P.1    Frankowska, H.2
  • 9
    • 84974160095 scopus 로고
    • An inversion theorem for set-valued maps
    • Azé D. An inversion theorem for set-valued maps. Bull. Austral. Math. Soc. 37:1988;411-414.
    • (1988) Bull. Austral. Math. Soc. , vol.37 , pp. 411-414
    • Azé, D.1
  • 10
    • 0008313997 scopus 로고
    • On a Newton type iterative method for solving inclusions
    • Azé D., Chou C. C. On a Newton type iterative method for solving inclusions. Math. Oper. Res. 20:1995;790-800.
    • (1995) Math. Oper. Res. , vol.20 , pp. 790-800
    • Azé, D.1    Chou, C.C.2
  • 12
    • 0041066876 scopus 로고
    • Two new open mapping theorems for analytic multivalued functions
    • Baribean L., Harbottle S. Two new open mapping theorems for analytic multivalued functions. Proc. Amer. Math. Soc. 115:1992;1009-1012.
    • (1992) Proc. Amer. Math. Soc. , vol.115 , pp. 1009-1012
    • Baribean, L.1    Harbottle, S.2
  • 13
    • 0022465886 scopus 로고
    • Stability and regular points of inequality systems
    • Borwein J. M. Stability and regular points of inequality systems. J. Optim. Theory Appl. 48:1986;9-52.
    • (1986) J. Optim. Theory Appl. , vol.48 , pp. 9-52
    • Borwein, J.M.1
  • 14
    • 38249029456 scopus 로고
    • Verifiable necessary and sufficient condition for openness and regularity of set-valued maps and single-valued maps
    • Borwein J. M., Zhuang D. M. Verifiable necessary and sufficient condition for openness and regularity of set-valued maps and single-valued maps. J. Math. Anal. Appl. 134:1988;441-459.
    • (1988) J. Math. Anal. Appl. , vol.134 , pp. 441-459
    • Borwein, J.M.1    Zhuang, D.M.2
  • 15
    • 0000650317 scopus 로고
    • A general principle on ordered sets in nonlinear functional analysis
    • Brézis H., Browder F. A general principle on ordered sets in nonlinear functional analysis. Adv. Math. 31:1976;355-364.
    • (1976) Adv. Math. , vol.31 , pp. 355-364
    • Brézis, H.1    Browder, F.2
  • 16
    • 0008563626 scopus 로고
    • Normal solvability and the Fredholm alternative for mappings into infinite dimensional manifolds
    • Browder F. E. Normal solvability and the Fredholm alternative for mappings into infinite dimensional manifolds. J. Funct. Anal. 8:1971;250-274.
    • (1971) J. Funct. Anal. , vol.8 , pp. 250-274
    • Browder, F.E.1
  • 17
    • 0041168190 scopus 로고
    • Inversion theorems for multifunctions in Fréchet spaces
    • Chou C. C. Inversion theorems for multifunctions in Fréchet spaces. Chinese J. Math. 19:1992;309-320.
    • (1992) Chinese J. Math. , vol.19 , pp. 309-320
    • Chou, C.C.1
  • 20
    • 0001303990 scopus 로고
    • Metric regularity, tangent sets, and second-order optimality conditions
    • Cominetti R. Metric regularity, tangent sets, and second-order optimality conditions. Appl. Math. Optim. 21:1990;265-287.
    • (1990) Appl. Math. Optim. , vol.21 , pp. 265-287
    • Cominetti, R.1
  • 21
    • 0001767025 scopus 로고
    • A geometric theorem useful in nonlinear functional analysis
    • Daneš J. A geometric theorem useful in nonlinear functional analysis. Boll. Un. Mat. Ital. 4:1972;369-375.
    • (1972) Boll. Un. Mat. Ital. , vol.4 , pp. 369-375
    • Daneš, J.1
  • 24
    • 0010890693 scopus 로고
    • Semicontinuity in constrained optimization. Part I. Metric spaces
    • Dolecki S. Semicontinuity in constrained optimization. Part I. Metric spaces. Control Cybernet. 7:1978;5-15.
    • (1978) Control Cybernet. , vol.7 , pp. 5-15
    • Dolecki, S.1
  • 25
    • 0010938187 scopus 로고
    • Semicontinuity in constrained optimization. Part Ib. Norm of spaces
    • Dolecki S. Semicontinuity in constrained optimization. Part Ib. Norm of spaces. Control Cybernet. 7:1978;17-26.
    • (1978) Control Cybernet , vol.7 , pp. 17-26
    • Dolecki, S.1
  • 27
    • 0016092731 scopus 로고
    • On the variational principle
    • Ekeland I. On the variational principle. J. Math. Anal. Appl. 47:1974;324-358.
    • (1974) J. Math. Anal. Appl. , vol.47 , pp. 324-358
    • Ekeland, I.1
  • 28
    • 38249033869 scopus 로고
    • An open mapping principle for set-valued maps
    • Frankowska H. An open mapping principle for set-valued maps. J. Math. Anal. Appl. 127:1987;172-180.
    • (1987) J. Math. Anal. Appl. , vol.127 , pp. 172-180
    • Frankowska, H.1
  • 29
    • 0038921735 scopus 로고
    • High order inverse function theorems
    • H. Attouch, J.-P. Aubin, & F. Clarke. Paris: C.R.M. Montréal and Gauthier-Villars
    • Frankowska H. High order inverse function theorems. Attouch H., Aubin J.-P., Clarke F. Analyse non linéaire, Contributions en l'honneur de J.-J. Moreau. 1987;283-303 C.R.M. Montréal and Gauthier-Villars, Paris.
    • (1987) Analyse Non Linéaire, Contributions en l'Honneur de J.-J. Moreau , pp. 283-303
    • Frankowska, H.1
  • 32
    • 84971134435 scopus 로고
    • Surjectivity of multifunctions under generalized differentiability assumptions
    • Gautier S., Isac G., Penot J.-P. Surjectivity of multifunctions under generalized differentiability assumptions. Bull. Austral. Math. Soc. 28:1983;13-21.
    • (1983) Bull. Austral. Math. Soc. , vol.28 , pp. 13-21
    • Gautier, S.1    Isac, G.2    Penot, J.-P.3
  • 33
    • 84972539529 scopus 로고
    • Some mapping theorems
    • Graves L. M. Some mapping theorems. Duke Math. J. 17:1950;111-114.
    • (1950) Duke Math. J. , vol.17 , pp. 111-114
    • Graves, L.M.1
  • 34
    • 84867959059 scopus 로고
    • Regular points of Lipschitz functions
    • Ioffe A. D. Regular points of Lipschitz functions. Trans. Amer. Math. Soc. 251:1979;61-69.
    • (1979) Trans. Amer. Math. Soc. , vol.251 , pp. 61-69
    • Ioffe, A.D.1
  • 35
    • 84966201346 scopus 로고
    • Nonsmooth analysis: Differential calculus of non-differentiable mappings
    • Ioffe A. D. Nonsmooth analysis: Differential calculus of non-differentiable mappings. Trans. Amer. Math. Soc. 266:1981;1-56.
    • (1981) Trans. Amer. Math. Soc. , vol.266 , pp. 1-56
    • Ioffe, A.D.1
  • 36
    • 0001413988 scopus 로고
    • On the local surjection property
    • Ioffe A. D. On the local surjection property. Nonlinear Anal. 11:1987;565-592.
    • (1987) Nonlinear Anal. , vol.11 , pp. 565-592
    • Ioffe, A.D.1
  • 38
    • 38249040136 scopus 로고
    • An induction theorem and general open mapping theorems
    • Khanh P. Q. An induction theorem and general open mapping theorems. J. Math. Anal. Appl. 118:1986;519-536.
    • (1986) J. Math. Anal. Appl. , vol.118 , pp. 519-536
    • Khanh, P.Q.1
  • 39
    • 38249028390 scopus 로고
    • An open mapping theorem for families of multifunctions
    • Khanh P. Q. An open mapping theorem for families of multifunctions. J. Math. Anal. Appl. 132:1988;491-498.
    • (1988) J. Math. Anal. Appl. , vol.132 , pp. 491-498
    • Khanh, P.Q.1
  • 40
    • 0000029197 scopus 로고
    • Preservation of convergence of convex sets and functions in finite dimensions
    • Mc Linden L., Bergström R. C. Preservation of convergence of convex sets and functions in finite dimensions. Trans. Amer. Math. Soc. 268:1981;127-140.
    • (1981) Trans. Amer. Math. Soc. , vol.268 , pp. 127-140
    • Mc Linden, L.1    Bergström, R.C.2
  • 41
    • 0000719894 scopus 로고
    • Conditional extrema of functionals
    • Liusternik L. A. Conditional extrema of functionals. Mat. Sb. 41:1934;390-401.
    • (1934) Mat. Sb. , vol.41 , pp. 390-401
    • Liusternik, L.A.1
  • 42
    • 84966250815 scopus 로고    scopus 로고
    • Complete characterizations of openness, metric regularity and Lipschitzian properties of multifunctions
    • B. Mordukhovich, Complete characterizations of openness, metric regularity and Lipschitzian properties of multifunctions, Trans. Amer. Math. Soc.
    • Trans. Amer. Math. Soc.
    • Mordukhovich, B.1
  • 43
    • 0020166855 scopus 로고
    • On regularity conditions in mathematical programming
    • Penot J.-P. On regularity conditions in mathematical programming. Math. Programming Study. 19:1982;167-199.
    • (1982) Math. Programming Study , vol.19 , pp. 167-199
    • Penot, J.-P.1
  • 44
    • 0021976215 scopus 로고
    • Open mappings theorems and linearization stability
    • Penot J.-P. Open mappings theorems and linearization stability. Numer. Funct. Anal. Optim. 8:1985;21-35.
    • (1985) Numer. Funct. Anal. Optim. , vol.8 , pp. 21-35
    • Penot, J.-P.1
  • 45
    • 0040574036 scopus 로고
    • About linearization, conization, calmness, openness and regularity
    • Lakshmikantham New York: Dekker
    • Penot J.-P. About linearization, conization, calmness, openness and regularity. Lakshmikantham. Nonlinear Analysis. 1987;439-450 Dekker, New York.
    • (1987) Nonlinear Analysis , pp. 439-450
    • Penot, J.-P.1
  • 46
    • 38249025950 scopus 로고
    • Metric regularity, openness and Lipschitzian behavior of multifunctions
    • Penot J.-P. Metric regularity, openness and Lipschitzian behavior of multifunctions. Nonlinear Anal. 13:1989;629-643.
    • (1989) Nonlinear Anal. , vol.13 , pp. 629-643
    • Penot, J.-P.1
  • 50
    • 0041173083 scopus 로고
    • Support cones and their generalizations
    • Providence: American Math. Soc. p. 393-401
    • Phelps R. R. Support cones and their generalizations. Proc. Symp. Pure Math. 1962;American Math. Soc. Providence. p. 393-401.
    • (1962) Proc. Symp. Pure Math.
    • Phelps, R.R.1
  • 51
    • 0039981138 scopus 로고
    • A quantitative refinement of the closed graph theorem
    • Pták V. A quantitative refinement of the closed graph theorem. Czechoslovak Math. J. 24:1974;503-506.
    • (1974) Czechoslovak Math. J. , vol.24 , pp. 503-506
    • Pták, V.1
  • 52
  • 53
    • 0007504078 scopus 로고
    • Mapping theorems for Gateaux differentiable and accretive operators
    • Ray W. O., Walker A. M. Mapping theorems for Gateaux differentiable and accretive operators. Nonlinear Anal. 6:1982;423-433.
    • (1982) Nonlinear Anal. , vol.6 , pp. 423-433
    • Ray, W.O.1    Walker, A.M.2
  • 54
    • 0016952838 scopus 로고
    • Regularity and stability for convex multivalued functions
    • Robinson S. M. Regularity and stability for convex multivalued functions. Math. Oper. Res. 1:1976;130-143.
    • (1976) Math. Oper. Res. , vol.1 , pp. 130-143
    • Robinson, S.M.1
  • 55
    • 0016993914 scopus 로고
    • Stability theorems for systems of inequalities. Part II. Differentiable nonlinear systems
    • Robinson S. M. Stability theorems for systems of inequalities. Part 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
  • 56
    • 0000676135 scopus 로고
    • Lipschitzian properties of multifunctions
    • Rockafellar R. T. Lipschitzian properties of multifunctions. Nonlinear Anal. 9:1985;867-885.
    • (1985) Nonlinear Anal. , vol.9 , pp. 867-885
    • Rockafellar, R.T.1
  • 57
    • 0000295695 scopus 로고
    • Generalized directional derivatives and subgradients of non convex functions
    • Rockafellar R. T. Generalized directional derivatives and subgradients of non convex functions. Canad. J. Math. 32:1980;157-181.
    • (1980) Canad. J. Math. , vol.32 , pp. 157-181
    • Rockafellar, R.T.1
  • 58
    • 0006496624 scopus 로고
    • Characterization of Clarke's tangent and normal cones in finite and infinite dimensions
    • Treiman J. S. Characterization of Clarke's tangent and normal cones in finite and infinite dimensions. Nonlinear Anal. 7:1983;771-783.
    • (1983) Nonlinear Anal. , vol.7 , pp. 771-783
    • Treiman, J.S.1
  • 59
    • 0001012728 scopus 로고
    • Multifunctions with closed convex graphs
    • Ursecu C. Multifunctions with closed convex graphs. Czechoslovak Math. J. 25:1975;438-449.
    • (1975) Czechoslovak Math. J. , vol.25 , pp. 438-449
    • Ursecu, C.1
  • 60
    • 0040904820 scopus 로고
    • Tangency and openness of multifunctions in Banach spaces
    • Ursescu C. Tangency and openness of multifunctions in Banach spaces. An. Ştiint. Univ. "Al. I. Cuza" Iasi. 34:1988;221-226.
    • (1988) An. Ştiint. Univ. "al. I. Cuza" Iasi , vol.34 , pp. 221-226
    • Ursescu, C.1
  • 61
    • 38249008119 scopus 로고
    • Some mapping theorems involving the perturbation ofm
    • Zen He. Some mapping theorems involving the perturbation ofm. Nonlinear Anal. 19:1992;345-351.
    • (1992) Nonlinear Anal. , vol.19 , pp. 345-351
    • Zen He1


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