On New Generalized Differentials with Respect to a Set and Their Applications

The notions and certain fundamental characteristics of the proximal and limiting normal cones with respect to a set are first presented in this paper. We present the ideas of the limiting coderivative and subdifferential with respect to a set of multifunctions and singleton mappings, respectively, b...

Celý popis

Uložené v:

Podrobná bibliografia
Vydané v:	Set-valued and variational analysis Ročník 32; číslo 3; s. 27
Hlavní autori:	Qin, Xiaolong, Duc Thinh, Vo, Yao, Jen-Chih
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Dordrecht Springer Netherlands 01.09.2024 Springer Nature B.V
Predmet:	Analysis Cones Constraining Euclidean space Mathematics Mathematics and Statistics Optimality criteria Optimization 90C31 Subdifferential with respect to a set 90C30 Aubin property with respect to a set 49J53 Coderivative with respect to a set Optimality condition Normal cone with respect to a set
ISSN:	1877-0533, 1877-0541
On-line prístup:	Získať plný text
Tagy:	Pridať tag Žiadne tagy, Buďte prvý, kto otaguje tento záznam!

Abstract	The notions and certain fundamental characteristics of the proximal and limiting normal cones with respect to a set are first presented in this paper. We present the ideas of the limiting coderivative and subdifferential with respect to a set of multifunctions and singleton mappings, respectively, based on these normal cones. The necessary and sufficient conditions for the Aubin property with respect to a set of multifunctions are then described by using the limiting coderivative with respect to a set. As a result of the limiting subdifferential with respect to a set, we offer the requisite optimality criteria for local solutions to optimization problems. In addition, we also provide examples to demonstrate the outcomes.
AbstractList	The notions and certain fundamental characteristics of the proximal and limiting normal cones with respect to a set are first presented in this paper. We present the ideas of the limiting coderivative and subdifferential with respect to a set of multifunctions and singleton mappings, respectively, based on these normal cones. The necessary and sufficient conditions for the Aubin property with respect to a set of multifunctions are then described by using the limiting coderivative with respect to a set. As a result of the limiting subdifferential with respect to a set, we offer the requisite optimality criteria for local solutions to optimization problems. In addition, we also provide examples to demonstrate the outcomes.
ArticleNumber	27
Author	Duc Thinh, Vo Yao, Jen-Chih Qin, Xiaolong
Author_xml	– sequence: 1 givenname: Xiaolong orcidid: 0000-0002-3381-8525 surname: Qin fullname: Qin, Xiaolong email: qxlxajh@163.com organization: Department of Mathematics, Zhejiang Normal University – sequence: 2 givenname: Vo surname: Duc Thinh fullname: Duc Thinh, Vo organization: Department of Mathematics, Zhejiang Normal University, Dong Thap University – sequence: 3 givenname: Jen-Chih surname: Yao fullname: Yao, Jen-Chih organization: Research Center for Interneural Computing, China Medical University Hospital
BookMark	eNp9kEtLQzEQhYMo2Kp_wFXA9dW87iPL4qMKakHrOsRkopGae01Siv313npFwUVXMwPnOzNzxmg3tAEQOqbklBJSnyVKGWsKwkTRj0wW6x00ok1dF6QUdPe353wfjVN660WESDpCd7OA72GFpxAg6oVfg8UX3jmIELLXi4RXPr_iB0gdmIxzizV-hIx1sHj-Cj7iSdctvNHZtyEdoj3XM3D0Uw_Q09Xl_Py6uJ1Nb84nt4Xhos6FrSrtjGwAalGBJsJVRgPnwnAHTW0Jt0YwUsKz4yAqbazU3EjLqZPWPZf8AJ0Mvl1sP5aQsnprlzH0KxVndcmkLAndqiKS05IJsvFqBpWJbUoRnDI-f7-To_YLRYnaRKyGiFUfsfqOWK17lP1Du-jfdfzcDvEBSr04vED8u2oL9QWGUpDi
CitedBy_id	crossref_primary_10_1007_s10957_024_02546_8 crossref_primary_10_1007_s10957_025_02761_x
Cites_doi	10.1137/22M151296X 10.1137/15M1052299 10.1007/3-540-31246-3 10.1007/s11117-011-0142-8 10.1007/978-1-4939-1037-3 10.1287/moor.2015.0741 10.1007/s11228-012-0220-5 10.1007/978-1-4612-1394-9 10.1007/s11784-010-0021-0 10.1080/00036811.2017.1408081 10.1007/s10479-017-2400-z 10.1007/978-3-642-02431-3 10.1007/s10107-020-01568-0 10.1137/S1052623496309296 10.1287/moor.20.3.695 10.1007/s11228-023-00698-9 10.1090/S0002-9947-1993-1156300-4 10.1007/s11228-018-0492-5
ContentType	Journal Article
Copyright	The Author(s), under exclusive licence to Springer Nature B.V. 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. The Author(s), under exclusive licence to Springer Nature B.V. 2024.
Copyright_xml	– notice: The Author(s), under exclusive licence to Springer Nature B.V. 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. – notice: The Author(s), under exclusive licence to Springer Nature B.V. 2024.
DBID	AAYXX CITATION 7XB 8FE 8FG ABJCF AFKRA AZQEC BENPR BGLVJ CCPQU DWQXO GNUQQ HCIFZ L6V M2P M7S PHGZM PHGZT PKEHL PQEST PQGLB PQQKQ PQUKI PTHSS Q9U
DOI	10.1007/s11228-024-00729-z
DatabaseName	CrossRef ProQuest Central (purchase pre-March 2016) ProQuest SciTech Collection ProQuest Technology Collection Materials Science & Engineering Collection ProQuest Central UK/Ireland ProQuest Central Essentials ProQuest Central Database Suite (ProQuest) Technology Collection ProQuest One Community College ProQuest Central Korea ProQuest Central Student SciTech Collection (ProQuest) ProQuest Engineering Collection Science Database Engineering Database Proquest Central Premium ProQuest One Academic (New) ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition Engineering Collection ProQuest Central Basic
DatabaseTitle	CrossRef Engineering Database ProQuest Central Student Technology Collection ProQuest Central Basic ProQuest One Academic Middle East (New) ProQuest Central Essentials ProQuest Science Journals ProQuest One Academic Eastern Edition SciTech Premium Collection ProQuest One Community College ProQuest Technology Collection ProQuest SciTech Collection ProQuest Central ProQuest One Applied & Life Sciences ProQuest Engineering Collection ProQuest One Academic UKI Edition ProQuest Central Korea Materials Science & Engineering Collection ProQuest One Academic ProQuest Central (New) Engineering Collection ProQuest One Academic (New)
DatabaseTitleList	Engineering Database
Database_xml	– sequence: 1 dbid: BENPR name: ProQuest Central url: https://www.proquest.com/central sourceTypes: Aggregation Database
DeliveryMethod	fulltext_linktorsrc
Discipline	Mathematics
EISSN	1877-0541
ExternalDocumentID	10_1007_s11228_024_00729_z
GrantInformation_xml	– fundername: National Natural Science Foundation of China grantid: 11401152 funderid: http://dx.doi.org/10.13039/501100001809
GroupedDBID	-5D -5G -BR -EM -Y2 -~C .VR 06D 0R~ 0VY 199 1N0 203 2J2 2JN 2JY 2KG 2LR 2~H 30V 4.4 406 408 409 40D 40E 5VS 6NX 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDZT ABECU ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSNA ACZOJ ADHIR ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFEXP AFGCZ AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AOCGG ARMRJ AXYYD AYJHY AZFZN B-. BAPOH BDATZ BGNMA BSONS CSCUP DDRTE DNIVK DPUIP DU5 EBLON EBS EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 H13 HF~ HG6 HLICF HMJXF HQYDN HRMNR HVGLF HZ~ IJ- IKXTQ ITM IWAJR IZIGR I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ KOV LAK LLZTM M4Y MA- N9A NB0 NPVJJ NQJWS NU0 O9- O93 O9G O9J P9R PF0 PT4 QOS R89 R9I ROL RSV S16 S3B SAP SCLPG SDH SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN TSG TSV TUC U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 YLTOR Z45 ZMTXR ZWQNP ~A9 AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC ADHKG AEZWR AFDZB AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP ATHPR AYFIA CITATION 7XB 8FE 8FG ABJCF AFKRA AZQEC BENPR BGLVJ CCPQU DWQXO GNUQQ HCIFZ L6V M2P M7S PHGZM PHGZT PKEHL PQEST PQGLB PQQKQ PQUKI PTHSS Q9U
ID	FETCH-LOGICAL-c347t-d66afc98ee746ea04f6cae334c3fe87d03dc4205ebf3e46acd9a3c9d31f9dfb53
IEDL.DBID	RSV
ISICitedReferencesCount	2
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001290691600001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	1877-0533
IngestDate	Tue Dec 02 06:50:58 EST 2025 Thu Sep 25 00:53:42 EDT 2025 Tue Nov 18 21:32:48 EST 2025 Sat Nov 29 01:59:32 EST 2025 Fri Feb 21 02:42:08 EST 2025
IsPeerReviewed	true
IsScholarly	true
Issue	3
Keywords	90C31 Subdifferential with respect to a set 90C30 Aubin property with respect to a set 49J53 Coderivative with respect to a set Optimality condition Normal cone with respect to a set
Language	English
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c347t-d66afc98ee746ea04f6cae334c3fe87d03dc4205ebf3e46acd9a3c9d31f9dfb53
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ORCID	0000-0002-3381-8525
PQID	3275299501
PQPubID	2044238
ParticipantIDs	proquest_journals_3275299501 proquest_journals_3093152405 crossref_citationtrail_10_1007_s11228_024_00729_z crossref_primary_10_1007_s11228_024_00729_z springer_journals_10_1007_s11228_024_00729_z
PublicationCentury	2000
PublicationDate	2024-09-01
PublicationDateYYYYMMDD	2024-09-01
PublicationDate_xml	– month: 09 year: 2024 text: 2024-09-01 day: 01
PublicationDecade	2020
PublicationPlace	Dordrecht
PublicationPlace_xml	– name: Dordrecht
PublicationSubtitle	Theory and Applications
PublicationTitle	Set-valued and variational analysis
PublicationTitleAbbrev	Set-Valued Var. Anal
PublicationYear	2024
Publisher	Springer Netherlands Springer Nature B.V
Publisher_xml	– name: Springer Netherlands – name: Springer Nature B.V
References	DontchevA.L.RockafellarR.T.Implicit Functions and Solution Mappings, a View from Variational Analysis20142New YorkSpringer10.1007/978-1-4939-1037-3 GfrererH.On directional metric regularity, subregularity and optimality conditions for non-smooth mathematical programsSet-Valued Var. Anal.201321151176304824110.1007/s11228-012-0220-5 BenkoM.GfrererH.OutrataJ.V.Calculus for directional limiting normal cones and subdifferentialsSet-Valued Var. Anal.201927713745399025110.1007/s11228-018-0492-5 MengK.W.LiM.H.YaoW.F.YangX.Q.Lipschitz-like property relative to a set and the generalized Mordukhovich criterionMath. Program.2021189455489430608110.1007/s10107-020-01568-0 ThinhV.D.ChuongT.D.Subdifferentials and derivatives with respect to a set and their applications to optimizationAppl. Anal.201998510051026391710910.1080/00036811.2017.1408081 ChuongT.D.KimD.S.Holder-like property and metric regularity of a positive-order for implicit multifunctionsMath. Oper. Res.201641596611348680910.1287/moor.2015.0741 MordukhovichB.S.Variational Analysis and Generalized Differentiation I: Basic Theory2006BerlinSpringer10.1007/3-540-31246-3 PoliquinR.A.RockafellarR.T.Tilt stability of a local minimumSIAM J. Optim.19988287299161879010.1137/S1052623496309296 YaoW.YangX.Relative Lipschitz-like property of parametric systems via projectional coderivativeSIAM J. Optim.2023320212040462328810.1137/22M151296X GinchevI.MordukhovichB.S.On directionally dependent subdifferentialsC. R. Acad. Bulgare Sci.2011644975082865674 IoffeA.D.On regularity concepts in variational analysisJ. Fixed Point Theory Appl.20108339363273902710.1007/s11784-010-0021-0 BonnansJ.F.ShapiroA.Perturbation Analysis of Optimization Problems20001New YorkSpringer10.1007/978-1-4612-1394-9 AubinJ.-P.FrankowskaH.Set-Valued Analysis1991BostonBirkhaüser ClarkeE.H.LedyaevY.S.StemR.J.WolenskiR.R.Nonsmooth Analysis and Control Theory1998New YorkSpringer GfrererH.OutrataJ.V.On Lipschitzian properties of implicit multifunctionsSIAM J. Optim.201626421602189356177810.1137/15M1052299 MordukhovichB.S.Complete characterization of openness, metric regularity, and Lipschitzian properties of multifunctionsTransl. Am. Math. Soc.19933401135115630010.1090/S0002-9947-1993-1156300-4 YenN.D.Lipschitz continuity of solutions of variational inequalities with a parametric polyhedral constraintMath. Oper. Res.199520695708135477710.1287/moor.20.3.695 GinchevI.MordukhovichB.S.Directional subdifferentials and optimality conditionsPositivity201216707737299408010.1007/s11117-011-0142-8 ThinhV.D.ChuongT.D.Directionally generalized differentiation for multifunctions and applications to set-valued programming problemsAnn. Oper. Res.2018269727751384850210.1007/s10479-017-2400-z RockafellarR.T.Convex Analysis1996PrincetonPrinceton University Press Yao, W., Meng, K., Li, M., Yang, X.: Projectional coderivatives and calculus rules. Set-Valued Var. Anal. 31 (2023) RockafellarR.T.WetR.-B.Variational Analysis1998BerlinSpringer10.1007/978-3-642-02431-3 V.D. Thinh (729_CR19) 2019; 98 E.H. Clarke (729_CR5) 1998 I. Ginchev (729_CR10) 2012; 16 B.S. Mordukhovich (729_CR14) 2006 R.A. Poliquin (729_CR15) 1998; 8 J.-P. Aubin (729_CR1) 1991 V.D. Thinh (729_CR18) 2018; 269 H. Gfrerer (729_CR7) 2013; 21 W. Yao (729_CR20) 2023; 3 B.S. Mordukhovich (729_CR13) 1993; 340 A.L. Dontchev (729_CR6) 2014 A.D. Ioffe (729_CR11) 2010; 8 H. Gfrerer (729_CR8) 2016; 26 N.D. Yen (729_CR22) 1995; 20 T.D. Chuong (729_CR4) 2016; 41 I. Ginchev (729_CR9) 2011; 64 R.T. Rockafellar (729_CR17) 1998 729_CR21 R.T. Rockafellar (729_CR16) 1996 M. Benko (729_CR2) 2019; 27 K.W. Meng (729_CR12) 2021; 189 J.F. Bonnans (729_CR3) 2000
References_xml	– reference: ChuongT.D.KimD.S.Holder-like property and metric regularity of a positive-order for implicit multifunctionsMath. Oper. Res.201641596611348680910.1287/moor.2015.0741 – reference: PoliquinR.A.RockafellarR.T.Tilt stability of a local minimumSIAM J. Optim.19988287299161879010.1137/S1052623496309296 – reference: BenkoM.GfrererH.OutrataJ.V.Calculus for directional limiting normal cones and subdifferentialsSet-Valued Var. Anal.201927713745399025110.1007/s11228-018-0492-5 – reference: ClarkeE.H.LedyaevY.S.StemR.J.WolenskiR.R.Nonsmooth Analysis and Control Theory1998New YorkSpringer – reference: YenN.D.Lipschitz continuity of solutions of variational inequalities with a parametric polyhedral constraintMath. Oper. Res.199520695708135477710.1287/moor.20.3.695 – reference: MordukhovichB.S.Complete characterization of openness, metric regularity, and Lipschitzian properties of multifunctionsTransl. Am. Math. Soc.19933401135115630010.1090/S0002-9947-1993-1156300-4 – reference: ThinhV.D.ChuongT.D.Directionally generalized differentiation for multifunctions and applications to set-valued programming problemsAnn. Oper. Res.2018269727751384850210.1007/s10479-017-2400-z – reference: BonnansJ.F.ShapiroA.Perturbation Analysis of Optimization Problems20001New YorkSpringer10.1007/978-1-4612-1394-9 – reference: MengK.W.LiM.H.YaoW.F.YangX.Q.Lipschitz-like property relative to a set and the generalized Mordukhovich criterionMath. Program.2021189455489430608110.1007/s10107-020-01568-0 – reference: Yao, W., Meng, K., Li, M., Yang, X.: Projectional coderivatives and calculus rules. Set-Valued Var. Anal. 31 (2023) – reference: DontchevA.L.RockafellarR.T.Implicit Functions and Solution Mappings, a View from Variational Analysis20142New YorkSpringer10.1007/978-1-4939-1037-3 – reference: AubinJ.-P.FrankowskaH.Set-Valued Analysis1991BostonBirkhaüser – reference: GfrererH.On directional metric regularity, subregularity and optimality conditions for non-smooth mathematical programsSet-Valued Var. Anal.201321151176304824110.1007/s11228-012-0220-5 – reference: IoffeA.D.On regularity concepts in variational analysisJ. Fixed Point Theory Appl.20108339363273902710.1007/s11784-010-0021-0 – reference: GfrererH.OutrataJ.V.On Lipschitzian properties of implicit multifunctionsSIAM J. Optim.201626421602189356177810.1137/15M1052299 – reference: MordukhovichB.S.Variational Analysis and Generalized Differentiation I: Basic Theory2006BerlinSpringer10.1007/3-540-31246-3 – reference: GinchevI.MordukhovichB.S.Directional subdifferentials and optimality conditionsPositivity201216707737299408010.1007/s11117-011-0142-8 – reference: RockafellarR.T.Convex Analysis1996PrincetonPrinceton University Press – reference: RockafellarR.T.WetR.-B.Variational Analysis1998BerlinSpringer10.1007/978-3-642-02431-3 – reference: GinchevI.MordukhovichB.S.On directionally dependent subdifferentialsC. R. Acad. Bulgare Sci.2011644975082865674 – reference: YaoW.YangX.Relative Lipschitz-like property of parametric systems via projectional coderivativeSIAM J. Optim.2023320212040462328810.1137/22M151296X – reference: ThinhV.D.ChuongT.D.Subdifferentials and derivatives with respect to a set and their applications to optimizationAppl. Anal.201998510051026391710910.1080/00036811.2017.1408081 – volume: 3 start-page: 2021 year: 2023 ident: 729_CR20 publication-title: SIAM J. Optim. doi: 10.1137/22M151296X – volume: 26 start-page: 2160 issue: 4 year: 2016 ident: 729_CR8 publication-title: SIAM J. Optim. doi: 10.1137/15M1052299 – volume-title: Variational Analysis and Generalized Differentiation I: Basic Theory year: 2006 ident: 729_CR14 doi: 10.1007/3-540-31246-3 – volume: 16 start-page: 707 year: 2012 ident: 729_CR10 publication-title: Positivity doi: 10.1007/s11117-011-0142-8 – volume-title: Implicit Functions and Solution Mappings, a View from Variational Analysis year: 2014 ident: 729_CR6 doi: 10.1007/978-1-4939-1037-3 – volume: 41 start-page: 596 year: 2016 ident: 729_CR4 publication-title: Math. Oper. Res. doi: 10.1287/moor.2015.0741 – volume: 21 start-page: 151 year: 2013 ident: 729_CR7 publication-title: Set-Valued Var. Anal. doi: 10.1007/s11228-012-0220-5 – volume-title: Perturbation Analysis of Optimization Problems year: 2000 ident: 729_CR3 doi: 10.1007/978-1-4612-1394-9 – volume: 8 start-page: 339 year: 2010 ident: 729_CR11 publication-title: J. Fixed Point Theory Appl. doi: 10.1007/s11784-010-0021-0 – volume: 98 start-page: 1005 issue: 5 year: 2019 ident: 729_CR19 publication-title: Appl. Anal. doi: 10.1080/00036811.2017.1408081 – volume: 269 start-page: 727 year: 2018 ident: 729_CR18 publication-title: Ann. Oper. Res. doi: 10.1007/s10479-017-2400-z – volume-title: Variational Analysis year: 1998 ident: 729_CR17 doi: 10.1007/978-3-642-02431-3 – volume-title: Set-Valued Analysis year: 1991 ident: 729_CR1 – volume: 189 start-page: 455 year: 2021 ident: 729_CR12 publication-title: Math. Program. doi: 10.1007/s10107-020-01568-0 – volume: 8 start-page: 287 year: 1998 ident: 729_CR15 publication-title: SIAM J. Optim. doi: 10.1137/S1052623496309296 – volume: 64 start-page: 497 year: 2011 ident: 729_CR9 publication-title: C. R. Acad. Bulgare Sci. – volume: 20 start-page: 695 year: 1995 ident: 729_CR22 publication-title: Math. Oper. Res. doi: 10.1287/moor.20.3.695 – volume-title: Convex Analysis year: 1996 ident: 729_CR16 – ident: 729_CR21 doi: 10.1007/s11228-023-00698-9 – volume: 340 start-page: 1 issue: 1 year: 1993 ident: 729_CR13 publication-title: Transl. Am. Math. Soc. doi: 10.1090/S0002-9947-1993-1156300-4 – volume: 27 start-page: 713 year: 2019 ident: 729_CR2 publication-title: Set-Valued Var. Anal. doi: 10.1007/s11228-018-0492-5 – volume-title: Nonsmooth Analysis and Control Theory year: 1998 ident: 729_CR5
SSID	ssj0070091
Score	2.3689563
Snippet	The notions and certain fundamental characteristics of the proximal and limiting normal cones with respect to a set are first presented in this paper. We...
SourceID	proquest crossref springer
SourceType	Aggregation Database Enrichment Source Index Database Publisher
StartPage	27
SubjectTerms	Analysis Cones Constraining Euclidean space Mathematics Mathematics and Statistics Optimality criteria Optimization
SummonAdditionalLinks	– databaseName: Science Database dbid: M2P link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV07T8MwELZ4DTDwRpSXPLCBRWI7cTIhBFQMFBAUqVvk2GcJCaVAA0N_PbbrtICgC7MTO8p3OX_x3X2H0KFJLAtXOiaZpRuEpwxImUlDqJaGSqpoJHyh8LW4ucl6vfwuHLgNQlpl4xO9o9Z95c7ITxgViXWdSRSfvrwS1zXKRVdDC41ZNG-Xil1KV4feNZ5YWP7gf7gyIYirOQ1FM6PSuZg6bWbKiRfPJsPvG9OEbf4IkPp9p73y3ydeRcuBceKzkYmsoRmo1tFSZyzXOthAndsKW2-Hgwb10xA0vgidU2pnoNgd1-J78HWZuO5jiR-gxrLSuOsiDfjsSxx8Ez22L7vnVyT0WSCKcVETnabSqDwDEDwFGXGTKgmMccUMZEJHTCtOowRKw4CnUulcMpVrFptcmzJhW2iu6lewjbAuS8lNKXViiVaccyl4roTTDAPIDfAWipuXXKggQu56YTwXE_lkB0xhgSk8MMWwhY7G97yMJDimXr3XoFGEz3FQuHCvJSqWnP4-PEaqhY4buCfDfy-2M322XbRIvYW5lLQ9NFe_vcM-WlAf9dPg7cDb6idXVe9h priority: 102 providerName: ProQuest
Title	On New Generalized Differentials with Respect to a Set and Their Applications
URI	https://link.springer.com/article/10.1007/s11228-024-00729-z https://www.proquest.com/docview/3093152405 https://www.proquest.com/docview/3275299501
Volume	32
WOSCitedRecordID	wos001290691600001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVAVX databaseName: SpringerLINK Contemporary 1997-Present customDbUrl: eissn: 1877-0541 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0070091 issn: 1877-0533 databaseCode: RSV dateStart: 20090601 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1NT-MwEB1B4QCHXT5FWbbygRtYSmwnTo7sAtoDLVULiFvk2GMJCQVEA4f-emw3oYBgJbjkYudD48nMS8bvDcC-TRwK1yammYMbVKQcaZkpS5lRlimmWSQDUfhMDgbZ9XU-bEhhk3a3e1uSDJF6TnaLmVdTZoIGuWs6XYQll-4y37BhNL5q4690qCF8ZmVSUs80bagyH1_jbTqaY8x3ZdGQbU5_fu851-BHgy7J0cwd1mEBqw1Y7b9Is042oX9eERfZSKM3fTNFQ46bLim1d0bif82SEQYOJqnviCJjrImqDLnwVQVy9KrmvQWXpycXf__RpqcC1VzImpo0VVbnGaIUKapI2FQr5FxobjGTJuJGCxYlWFqOIlXa5Irr3PDY5saWCd-GTnVX4Q4QU5ZK2FKZxIGqOBdKilxLrw-GmFsUXYhb0xa6ERz3fS9ui7lUsjdV4UxVBFMV0y4cvJxzP5Pb-O_svXbFiubVmxS-tOtAiQOiHw8zmbgUnERxFw7bBZwPf36z3a9N_wUrLPiA3462B5364RF_w7J-qm8mDz1Y-nMyGI56sNhnQ3-U417w4md78ems
linkProvider	Springer Nature
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Nb9QwEB1VBQk48F2xUMAHOIFFYjtxcqiqilK16u5SwSL1Fhx7LFVC2dINIPZH9TfW4012AUFvPXB2PpT4-fnZ43kD8MJnQYVbl_IiyA2ucom8LoznwhkvjLAi0TFReKjH4-L4uDxag_M-F4aOVfacGInaTS3tkb-RQmeBOrMk3T79yqlqFEVX-xIaC1gc4s8fYck22zrYDf37Uoi9d5O3-7yrKsCtVLrlLs-Nt2WBqFWOJlE-twalVFZ6LLRLpLNKJBnWXqLKjXWlkbZ0MvWl8zVViQiUf02RsxgdFRRHPfProFfiAq_QmlOOa5eks0jVSwV5QQvFo1k3n_8-Ea7U7R8B2TjP7d353_7QXbjdKWq2sxgC92ANm_twa7S0o509gNH7hgU2Z53H9skcHdvtKsO0NAAZbUezDxjzTlk7ZYZ9xJaZxrEJRVLYzi9x_ofw6Uq-ZwPWm2mDj4C5ujbK18ZlQUimpTJalVaTJxpi6VENIO07tbKdyTrV-vhSreyhCQhVAEIVgVDNB_Bqec_pwmLk0qs3-96vOrqZVRTODkIsiO-_Ny-RMYDXPbxWzf9-2ePLn_YcbuxPRsNqeDA-fAI3RUQ3Hb_bhPX27Bs-hev2e3syO3sWxwmDz1cNuwstelCx
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LT9wwEB7RparKAfqg6vKqD721FontxPFxBaxAwBYVWnGLHHssrVQFtJv2sL8e25uwC6JIVc92HhpPPJ8z830D8NllHoUbm9LCww0qco60KrSjzGrHNDMskZEofCZHo-L6Wl0ssfhjtXuXkpxzGoJKU93s31q3vyC-pSwoKzNBo_Q1nb2AVREK6cN5_fJntxdLjyDikauQkgbWaUubefoeD0PTAm8-SpHGyDPc-P93fgPrLeokg7mbvIUVrN_B2vm9ZOv0PZx_q4nf8UirQz2eoSWHbfeUJjgpCb9syXeM3EzS3BBNLrEhurbkKmQbyGApF74JP4ZHVwfHtO21QA0XsqE2z7UzqkCUIkedCJcbjZwLwx0W0ibcGsGSDCvHUeTaWKW5UZanTllXZfwD9OqbGj8CsVWlhau0zTzYSpXQUigjg24YonIo-pB2Zi5NK0Qe-mH8KhcSysFUpTdVGU1Vzvrw5f6a27kMx7Ozd7rVK9tPclqGlK8HKx6gPj3MZOZDc5akffjaLeZi-O8P2_q36Z_g1cXhsDw7GZ1uw2sW3SFUrO1Ar5n8xl14af404-lkLzryHW_k8fI
openUrl	ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=On+New+Generalized+Differentials+with+Respect+to+a+Set+and+Their+Applications&rft.jtitle=Set-valued+and+variational+analysis&rft.au=Qin+Xiaolong&rft.au=Vo%2C+Duc+Thinh&rft.au=Yao+Jen-Chih&rft.date=2024-09-01&rft.pub=Springer+Nature+B.V&rft.issn=1877-0533&rft.eissn=1877-0541&rft.volume=32&rft.issue=3&rft_id=info:doi/10.1007%2Fs11228-024-00729-z&rft.externalDBID=NO_FULL_TEXT
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1877-0533&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1877-0533&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1877-0533&client=summon