A note on implicit multifunction theorems
The paper is mainly devoted to the study of implicit multifunction theorems in terms of Fréchet coderivative in Asplund spaces. It sharpens the well-known implicit multifunction theorem of Ledyaev and Zhu (Set Valued Anal., 7, 209–238, 1999 ) as well as many recent publications about this significan...
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| Vydáno v: | Optimization letters Ročník 8; číslo 1; s. 329 - 341 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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01.01.2014
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| ISSN: | 1862-4472, 1862-4480 |
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| Abstract | The paper is mainly devoted to the study of implicit multifunction theorems in terms of Fréchet coderivative in Asplund spaces. It sharpens the well-known implicit multifunction theorem of Ledyaev and Zhu (Set Valued Anal., 7, 209–238,
1999
) as well as many recent publications about this significant area. |
|---|---|
| AbstractList | The paper is mainly devoted to the study of implicit multifunction theorems in terms of Fréchet coderivative in Asplund spaces. It sharpens the well-known implicit multifunction theorem of Ledyaev and Zhu (Set Valued Anal., 7, 209–238,
1999
) as well as many recent publications about this significant area. |
| Author | Nghia, T. T. A. |
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| Cites_doi | 10.1023/A:1008775413250 10.1023/B:SVAN.0000023394.19482.30 10.1016/j.na.2011.06.005 10.1007/s11228-008-0072-1 10.1070/RM2000v055n03ABEH000292 10.1137/090772174 10.1080/00036811.2010.483432 10.1016/j.na.2008.04.005 10.1007/978-0-387-87821-8 10.1016/0022-247X(74)90025-0 10.1023/B:SVAN.0000023396.58424.98 10.1016/j.na.2009.12.039 10.1016/j.jmaa.2007.05.001 10.1137/0713043 10.1137/0712056 10.1137/S0363012998339216 10.1007/s10898-011-9651-z 10.1016/j.na.2009.06.105 10.1007/3-540-31246-3 10.1007/3-540-31247-1 |
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| Keywords | Implicit multifunction theorem Metric subregularity Metric regularity 49J53 49J52 Fréchet coderivative |
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| References | Mordukhovich (CR16) 1980; 254 Yen, Yao (CR24) 2009; 70 Azé, Benahmed (CR1) 2008; 16 CR15 Chuong, Kruger, Yao (CR4) 2011; 51 Durea (CR7) 2010; 72 Lee, Tam, Yen (CR12) 2008; 338 Jourani (CR11) 2000; 38 Mordukhovich (CR18) 2006 Dontchev, Rockafellar (CR5) 2004; 12 Chuong (CR3) 2011; 74 Phelps (CR21) 1993 Lee, Yen (CR13) 2011; 90 Robinson (CR23) 1976; 13 Mordukhovich (CR17) 2006 Zheng, Ng (CR25) 2010; 20 CR20 Ioffe (CR10) 2000; 55 Chieu, Yao, Yen (CR2) 2010; 72 Robinson (CR22) 1975; 12 Ledyaev, Zhu (CR14) 1999; 7 Fabian (CR9) 1989; 30 Ngai, Théra (CR19) 2004; 12 Dontchev, Rockafellar (CR6) 2009 Ekeland (CR8) 1970; 47 M Durea (580_CR7) 2010; 72 580_CR20 SM Robinson (580_CR22) 1975; 12 BS Mordukhovich (580_CR17) 2006 M Fabian (580_CR9) 1989; 30 YS Ledyaev (580_CR14) 1999; 7 TD Chuong (580_CR3) 2011; 74 SM Robinson (580_CR23) 1976; 13 I Ekeland (580_CR8) 1970; 47 AD Ioffe (580_CR10) 2000; 55 580_CR15 D Azé (580_CR1) 2008; 16 A Jourani (580_CR11) 2000; 38 ND Yen (580_CR24) 2009; 70 GM Lee (580_CR13) 2011; 90 TD Chuong (580_CR4) 2011; 51 NH Chieu (580_CR2) 2010; 72 BS Mordukhovich (580_CR16) 1980; 254 HV Ngai (580_CR19) 2004; 12 AL Dontchev (580_CR5) 2004; 12 BS Mordukhovich (580_CR18) 2006 GM Lee (580_CR12) 2008; 338 XY Zheng (580_CR25) 2010; 20 AL Dontchev (580_CR6) 2009 RR Phelps (580_CR21) 1993 |
| References_xml | – volume: 7 start-page: 209 year: 1999 end-page: 238 ident: CR14 article-title: Implicit multifunction theorems publication-title: Set Valued Anal. doi: 10.1023/A:1008775413250 – volume: 12 start-page: 79 year: 2004 end-page: 109 ident: CR5 article-title: Regularity and conditioning of solution mappings in variational analysis publication-title: Set Valued Anal. doi: 10.1023/B:SVAN.0000023394.19482.30 – volume: 74 start-page: 6256 year: 2011 end-page: 6264 ident: CR3 article-title: Lipschitz-like property of an implicit multifunction and its applications publication-title: Nonlinear Anal. doi: 10.1016/j.na.2011.06.005 – year: 1993 ident: CR21 publication-title: Convex Functions, Monotone Operators and Differentiability – volume: 16 start-page: 129 year: 2008 end-page: 155 ident: CR1 article-title: On implicit multifunction theorems publication-title: Set Valued Anal. doi: 10.1007/s11228-008-0072-1 – year: 2006 ident: CR18 publication-title: Variational Analysis and Generalized Differentiation, II: Applications – volume: 30 start-page: 51 year: 1989 end-page: 56 ident: CR9 article-title: Subdifferentiability and trustworthiness in the light of a new variational principle of Borwein and Preiss publication-title: Acta Univ. 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Anal. doi: 10.1137/0712056 – ident: 580_CR20 – volume: 20 start-page: 2119 year: 2010 ident: 580_CR25 publication-title: SIAM J. Optim. doi: 10.1137/090772174 – volume: 338 start-page: 11 year: 2008 ident: 580_CR12 publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2007.05.001 – volume: 90 start-page: 1011 year: 2011 ident: 580_CR13 publication-title: Appl. Anal. doi: 10.1080/00036811.2010.483432 – volume: 72 start-page: 3594 year: 2010 ident: 580_CR2 publication-title: Nonlinear Anal. doi: 10.1016/j.na.2009.12.039 – volume: 12 start-page: 79 year: 2004 ident: 580_CR5 publication-title: Set Valued Anal. doi: 10.1023/B:SVAN.0000023394.19482.30 – volume: 74 start-page: 6256 year: 2011 ident: 580_CR3 publication-title: Nonlinear Anal. doi: 10.1016/j.na.2011.06.005 – volume-title: Variational Analysis and Generalized Differentiation, II: Applications year: 2006 ident: 580_CR18 doi: 10.1007/3-540-31246-3 – volume-title: Implicit functions and solution mappings. 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| Title | A note on implicit multifunction theorems |
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