DIRECTIONAL COMPACTNESS, SCALARIZATION AND NONSMOOTH SEMI-FREDHOLM MAPPINGS
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| Published in: | Nonlinear analysis Vol. 29; no. 2; pp. 201 - 219 |
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| Format: | Journal Article |
| Language: | English |
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Elsevier Ltd
01.07.1997
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| ISSN: | 0362-546X, 1873-5215 |
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| Author | IOFFE, A.D. |
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| References | MORDUKHOVICH (BIB15) 1976; 40 JOURANI, THIBAULT (BIB16) 1993; 47 PENOT J.P., Compactness property, openness criteria and coderivatives. (Preprint, 1995.) BORWEIN J. & ZHU J., Viscosity solutions and viscosity subderivatives in smooth Banach spaces with applications to metric regularity Nauka, Moscow (1988). (In Russian; English translation to be published by Wiley Interscience.) JOURANI, THIBAULT (BIB5) 1995; 347 LOEWEN P.D., Limits of Fréchet normals in nonsmooth analysis, in JOURANI A. & THIBAULT L., Metric regularity and strongly compactly Lipschitzean mappings IOFFE (BIB11) 1984; 10 BORWEIN, IOFFE (BIB17) 1996; 4 MORDUKHOVICH B. & YONGHENG SHAO, Stability of set-valued mappings in infinite dimension: point criteria and applications IOFFE (BIB13) 1990; 41 IOFFE (BIB19) 1984; 8 IOFFE (BIB20) 1996; 323 THIBAULT (BIB22) 1980; 125 GINSBURG B. & IOFFE A., The maximum principle in optimal control of systems governed by semilinear equations. 9, 159–189 (1984) IOFFE (BIB21) 1981; 266 Minneapolis 1993 (Edited by B. MORDUKHOVICH and H. SUSSMAN). Springer. (To appear.) GLOVER B.M. & CRAVEN B.D., A Fritz John optimality condition using the approximate subdifferential. (Preprint, 1992.) IOFFE A., Codirectional compactness and metric regularity of set-valued mappings. (In preparation.). IOFFE (BIB14) 1981; 292 MORDUKHOVICH B. IOFFE A., Nonsmooth subdifferentials: their calculus and applications. (Edited by A. IOFFE, M. MARCUS and S. REICH), pp. 178–188. Longman, Essex (1992). Tampa, 1991. de Gruyter, New York, pp. 2299–2310 (1996). KRUGER (BIB25) 1985; 26 To appear. JOURANI, THIBAULT (BIB28) 1994; 49 MORDUKHOVICH, YONGHENG (BIB6) 1996; 348 IOFFE A., Necessary conditions in nonsmooth optimization FABIAN (BIB26) 1989; 30 IOFFE (BIB2) 1987; 11 11, 565–592 (1987). IOFFE (BIB1) 1984; 281 IOFFE (BIB3) 1989; 36 BORWEIN, STROJWAS (BIB29) 1985; 9 IOFFE (10.1016/S0362-546X(96)00046-6_BIB13) 1990; 41 BORWEIN (10.1016/S0362-546X(96)00046-6_BIB17) 1996; 4 10.1016/S0362-546X(96)00046-6_BIB18 MORDUKHOVICH (10.1016/S0362-546X(96)00046-6_BIB6) 1996; 348 MORDUKHOVICH (10.1016/S0362-546X(96)00046-6_BIB15) 1976; 40 BORWEIN (10.1016/S0362-546X(96)00046-6_BIB29) 1985; 9 JOURANI (10.1016/S0362-546X(96)00046-6_BIB28) 1994; 49 IOFFE (10.1016/S0362-546X(96)00046-6_BIB19) 1984; 8 JOURANI (10.1016/S0362-546X(96)00046-6_BIB16) 1993; 47 IOFFE (10.1016/S0362-546X(96)00046-6_BIB11) 1984; 10 JOURANI (10.1016/S0362-546X(96)00046-6_BIB5) 1995; 347 10.1016/S0362-546X(96)00046-6_BIB24 10.1016/S0362-546X(96)00046-6_BIB23 10.1016/S0362-546X(96)00046-6_BIB27 10.1016/S0362-546X(96)00046-6_BIB9 10.1016/S0362-546X(96)00046-6_BIB7 10.1016/S0362-546X(96)00046-6_BIB8 KRUGER (10.1016/S0362-546X(96)00046-6_BIB25) 1985; 26 IOFFE (10.1016/S0362-546X(96)00046-6_BIB1) 1984; 281 10.1016/S0362-546X(96)00046-6_BIB4 IOFFE (10.1016/S0362-546X(96)00046-6_BIB3) 1989; 36 IOFFE (10.1016/S0362-546X(96)00046-6_BIB20) 1996; 323 IOFFE (10.1016/S0362-546X(96)00046-6_BIB21) 1981; 266 IOFFE (10.1016/S0362-546X(96)00046-6_BIB2) 1987; 11 FABIAN (10.1016/S0362-546X(96)00046-6_BIB26) 1989; 30 10.1016/S0362-546X(96)00046-6_BIB30 10.1016/S0362-546X(96)00046-6_BIB10 10.1016/S0362-546X(96)00046-6_BIB12 THIBAULT (10.1016/S0362-546X(96)00046-6_BIB22) 1980; 125 IOFFE (10.1016/S0362-546X(96)00046-6_BIB14) 1981; 292 |
| References_xml | – reference: GINSBURG B. & IOFFE A., The maximum principle in optimal control of systems governed by semilinear equations. – reference: PENOT J.P., Compactness property, openness criteria and coderivatives. (Preprint, 1995.) – volume: 4 start-page: 1 year: 1996 end-page: 24 ident: BIB17 article-title: Proximal analysis in smooth spaces publication-title: Set-Valued Analysis – reference: IOFFE A., Nonsmooth subdifferentials: their calculus and applications. – volume: 266 start-page: 1 year: 1981 end-page: 56 ident: BIB21 article-title: Nonsmooth analysis: differential calculus of nondifferentiable mappings publication-title: Trans. Am. math. Soc. – reference: BORWEIN J. & ZHU J., Viscosity solutions and viscosity subderivatives in smooth Banach spaces with applications to metric regularity, – reference: IOFFE A., Codirectional compactness and metric regularity of set-valued mappings. (In preparation.). – volume: 41 start-page: 175 year: 1990 end-page: 192 ident: BIB13 article-title: Proximal analysis and approximate subdifferentials publication-title: J. London math. Soc. – volume: 40 start-page: 960 year: 1976 end-page: 969 ident: BIB15 article-title: Maximum principle in an optimal time control problem with nonsmooth constraints publication-title: J. Appl. Math. Mech. – volume: 281 start-page: 289 year: 1984 end-page: 316 ident: BIB1 article-title: Approximate subdifferentials and applications—1. The finite dimensional theory publication-title: Trans. Am. math Soc. – volume: 47 start-page: 443 year: 1993 end-page: 455 ident: BIB16 article-title: The approximate subdifferential of a composite function publication-title: Bull. Aust. Math. Soc. – volume: 347 start-page: 443 year: 1995 end-page: 455 ident: BIB5 article-title: Verifiable conditions for openness and regularity of multivalued mappings publication-title: Trans. Am. math. Soc. – reference: (Edited by A. IOFFE, M. MARCUS and S. REICH), pp. 178–188. Longman, Essex (1992). – reference: . (To appear.) – volume: 348 start-page: 1235 year: 1996 end-page: 1280 ident: BIB6 article-title: Nonsmooth sequential analysis in Asplund spaces publication-title: Trans. Am. math. Soc. – volume: 323 start-page: 107 year: 1996 end-page: 112 ident: BIB20 article-title: Separable reduction theorem for approximate subdifferentials publication-title: C. r. Acad. Sci. Paris – reference: JOURANI A. & THIBAULT L., Metric regularity and strongly compactly Lipschitzean mappings, – reference: MORDUKHOVICH B., – volume: 49 start-page: 111 year: 1994 end-page: 116 ident: BIB28 article-title: A note on Fréchet and approximate subdifferentials of composite functions publication-title: Bull. Austr. math. Soc. – volume: 292 start-page: 675 year: 1981 end-page: 678 ident: BIB14 article-title: Sous-differentielles approchées de fonctions numériques publication-title: C. r. Acad. Sci. Paris – reference: , Minneapolis 1993 (Edited by B. MORDUKHOVICH and H. SUSSMAN). Springer. (To appear.) – volume: 9 start-page: 1347 year: 1985 end-page: 1366 ident: BIB29 article-title: Tangential approximations publication-title: Nonlinear Analysis – volume: 11 start-page: 565 year: 1987 end-page: 592 ident: BIB2 article-title: On the local surjection property publication-title: Nonlinear Analysis – reference: (To appear.) – volume: 125 start-page: 157 year: 1980 end-page: 192 ident: BIB22 article-title: Subdifferentials of compactly Lipschitzean vector-valued functions publication-title: Ann. Math. Pura ed Applicata – reference: . Nauka, Moscow (1988). (In Russian; English translation to be published by Wiley Interscience.) – volume: 10 start-page: 87 year: 1984 end-page: 89 ident: BIB11 article-title: Subdifferentiability spaces and nonsmooth analysis publication-title: Bull. Am. math. Soc. – reference: MORDUKHOVICH B. & YONGHENG SHAO, Stability of set-valued mappings in infinite dimension: point criteria and applications, – reference: 9, 159–189 (1984); – volume: 30 start-page: 51 year: 1989 end-page: 56 ident: BIB26 article-title: Subdifferentiability and trustworthiness in the light of the new variational principle of Borwein and Preiss publication-title: Acta Univ. Carolinae – reference: LOEWEN P.D., Limits of Fréchet normals in nonsmooth analysis, in – volume: 36 start-page: 1 year: 1989 end-page: 38 ident: BIB3 article-title: Approximate subdifferentials and applications—3. The metric theory publication-title: Mathematika – reference: GLOVER B.M. & CRAVEN B.D., A Fritz John optimality condition using the approximate subdifferential. (Preprint, 1992.) – reference: . 11, 565–592 (1987). – volume: 8 start-page: 517 year: 1984 end-page: 539 ident: BIB19 article-title: Calculus of Dini subdifferentials of functions and contingent derivatives of set-valued maps publication-title: Nonlinear Analysis – volume: 26 start-page: 370 year: 1985 end-page: 379 ident: BIB25 article-title: Generalized differentials of nonsmooth functions and necessary conditions for an extremum, publication-title: Siberian math. J. – reference: IOFFE A., Necessary conditions in nonsmooth optimization, – reference: , Tampa, 1991. de Gruyter, New York, pp. 2299–2310 (1996). – volume: 9 start-page: 1347 year: 1985 ident: 10.1016/S0362-546X(96)00046-6_BIB29 article-title: Tangential approximations publication-title: Nonlinear Analysis doi: 10.1016/0362-546X(85)90095-1 – volume: 292 start-page: 675 year: 1981 ident: 10.1016/S0362-546X(96)00046-6_BIB14 article-title: Sous-differentielles approchées de fonctions numériques publication-title: C. r. Acad. Sci. Paris – volume: 11 start-page: 565 year: 1987 ident: 10.1016/S0362-546X(96)00046-6_BIB2 article-title: On the local surjection property publication-title: Nonlinear Analysis doi: 10.1016/0362-546X(87)90073-3 – ident: 10.1016/S0362-546X(96)00046-6_BIB18 – volume: 49 start-page: 111 year: 1994 ident: 10.1016/S0362-546X(96)00046-6_BIB28 article-title: A note on Fréchet and approximate subdifferentials of composite functions publication-title: Bull. Austr. math. Soc. doi: 10.1017/S0004972700016142 – ident: 10.1016/S0362-546X(96)00046-6_BIB10 – ident: 10.1016/S0362-546X(96)00046-6_BIB4 – volume: 125 start-page: 157 year: 1980 ident: 10.1016/S0362-546X(96)00046-6_BIB22 article-title: Subdifferentials of compactly Lipschitzean vector-valued functions publication-title: Ann. Math. Pura ed Applicata doi: 10.1007/BF01789411 – ident: 10.1016/S0362-546X(96)00046-6_BIB8 – volume: 40 start-page: 960 year: 1976 ident: 10.1016/S0362-546X(96)00046-6_BIB15 article-title: Maximum principle in an optimal time control problem with nonsmooth constraints publication-title: J. Appl. Math. Mech. doi: 10.1016/0021-8928(76)90136-2 – ident: 10.1016/S0362-546X(96)00046-6_BIB27 – volume: 36 start-page: 1 year: 1989 ident: 10.1016/S0362-546X(96)00046-6_BIB3 article-title: Approximate subdifferentials and applications—3. The metric theory publication-title: Mathematika doi: 10.1112/S0025579300013541 – volume: 47 start-page: 443 year: 1993 ident: 10.1016/S0362-546X(96)00046-6_BIB16 article-title: The approximate subdifferential of a composite function publication-title: Bull. Aust. Math. Soc. doi: 10.1017/S0004972700015276 – ident: 10.1016/S0362-546X(96)00046-6_BIB23 – volume: 281 start-page: 289 year: 1984 ident: 10.1016/S0362-546X(96)00046-6_BIB1 article-title: Approximate subdifferentials and applications—1. The finite dimensional theory publication-title: Trans. Am. math Soc. – volume: 323 start-page: 107 year: 1996 ident: 10.1016/S0362-546X(96)00046-6_BIB20 article-title: Separable reduction theorem for approximate subdifferentials publication-title: C. r. Acad. Sci. Paris – volume: 10 start-page: 87 year: 1984 ident: 10.1016/S0362-546X(96)00046-6_BIB11 article-title: Subdifferentiability spaces and nonsmooth analysis publication-title: Bull. Am. math. Soc. doi: 10.1090/S0273-0979-1984-15194-2 – volume: 4 start-page: 1 year: 1996 ident: 10.1016/S0362-546X(96)00046-6_BIB17 article-title: Proximal analysis in smooth spaces publication-title: Set-Valued Analysis doi: 10.1007/BF00419371 – volume: 30 start-page: 51 year: 1989 ident: 10.1016/S0362-546X(96)00046-6_BIB26 article-title: Subdifferentiability and trustworthiness in the light of the new variational principle of Borwein and Preiss publication-title: Acta Univ. Carolinae – ident: 10.1016/S0362-546X(96)00046-6_BIB9 – ident: 10.1016/S0362-546X(96)00046-6_BIB12 doi: 10.1137/S0363012994268801 – ident: 10.1016/S0362-546X(96)00046-6_BIB30 – volume: 266 start-page: 1 year: 1981 ident: 10.1016/S0362-546X(96)00046-6_BIB21 article-title: Nonsmooth analysis: differential calculus of nondifferentiable mappings publication-title: Trans. Am. math. Soc. doi: 10.1090/S0002-9947-1981-0613784-7 – volume: 347 start-page: 443 year: 1995 ident: 10.1016/S0362-546X(96)00046-6_BIB5 article-title: Verifiable conditions for openness and regularity of multivalued mappings publication-title: Trans. Am. math. Soc. doi: 10.2307/2154809 – volume: 348 start-page: 1235 year: 1996 ident: 10.1016/S0362-546X(96)00046-6_BIB6 article-title: Nonsmooth sequential analysis in Asplund spaces publication-title: Trans. Am. math. Soc. doi: 10.1090/S0002-9947-96-01543-7 – volume: 41 start-page: 175 year: 1990 ident: 10.1016/S0362-546X(96)00046-6_BIB13 article-title: Proximal analysis and approximate subdifferentials publication-title: J. London math. Soc. doi: 10.1112/jlms/s2-41.1.175 – ident: 10.1016/S0362-546X(96)00046-6_BIB7 – volume: 8 start-page: 517 year: 1984 ident: 10.1016/S0362-546X(96)00046-6_BIB19 article-title: Calculus of Dini subdifferentials of functions and contingent derivatives of set-valued maps publication-title: Nonlinear Analysis doi: 10.1016/0362-546X(84)90091-9 – ident: 10.1016/S0362-546X(96)00046-6_BIB24 – volume: 26 start-page: 370 year: 1985 ident: 10.1016/S0362-546X(96)00046-6_BIB25 article-title: Generalized differentials of nonsmooth functions and necessary conditions for an extremum, publication-title: Siberian math. J. doi: 10.1007/BF00968624 |
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| Title | DIRECTIONAL COMPACTNESS, SCALARIZATION AND NONSMOOTH SEMI-FREDHOLM MAPPINGS |
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