Differential Stability of Convex Optimization Problems with Possibly Empty Solution Sets

This paper studies differential stability of infinite-dimensional convex optimization problems, whose solution sets may be empty. By using suitable sum rules for ε -subdifferentials, we obtain exact formulas for computing the ε -subdifferential of the optimal value function. Several illustrative exa...

Celý popis

Uložené v:

Podrobná bibliografia
Vydané v:	Journal of optimization theory and applications Ročník 181; číslo 1; s. 126 - 143
Hlavní autori:	An, Duong Thi Viet, Yao, Jen-Chih
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York Springer US 01.04.2019 Springer Nature B.V
Predmet:	Applications of Mathematics Calculus of Variations and Optimal Control; Optimization Computational geometry Convex analysis Convexity Dimensional stability Engineering Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Sum rules Theory of Computation 90C31 Optimal value function Subdifferentials 49J53 90C25 Conjugate function Parametric convex programming 49Q12 Normal directions
ISSN:	0022-3239, 1573-2878
On-line prístup:	Získať plný text
Tagy:	Pridať tag Žiadne tagy, Buďte prvý, kto otaguje tento záznam!

Abstract	This paper studies differential stability of infinite-dimensional convex optimization problems, whose solution sets may be empty. By using suitable sum rules for ε -subdifferentials, we obtain exact formulas for computing the ε -subdifferential of the optimal value function. Several illustrative examples are also given.
AbstractList	This paper studies differential stability of infinite-dimensional convex optimization problems, whose solution sets may be empty. By using suitable sum rules for ε -subdifferentials, we obtain exact formulas for computing the ε -subdifferential of the optimal value function. Several illustrative examples are also given. This paper studies differential stability of infinite-dimensional convex optimization problems, whose solution sets may be empty. By using suitable sum rules for \[\varepsilon \]-subdifferentials, we obtain exact formulas for computing the \[\varepsilon \]-subdifferential of the optimal value function. Several illustrative examples are also given.
Author	An, Duong Thi Viet Yao, Jen-Chih
Author_xml	– sequence: 1 givenname: Duong Thi Viet surname: An fullname: An, Duong Thi Viet organization: Department of Mathematics and Informatics, Thai Nguyen University of Sciences – sequence: 2 givenname: Jen-Chih surname: Yao fullname: Yao, Jen-Chih email: yaojc@mail.cmu.edu.tw organization: Center for General Education, China Medical University
BookMark	eNp9kF1LwzAUhoNMcJv-AO8CXldzkrZpL2XODxg4mIJ3IW0TzWibmmTq_PV2qyAIenVu3ue8L88EjVrbKoROgZwDIfzCA8kTHhHIIogZRHCAxpBwFtGMZyM0JoTSiFGWH6GJ92tCSJ7xeIyerozWyqk2GFnjVZCFqU3YYqvxzLZv6gPfd8E05lMGY1u8dLaoVePxuwkveGm9N0W9xfOm65mVrTf71EoFf4wOtay9Ovm-U_R4PX-Y3UaL-5u72eUiKhmkIdLAYigKFucEyrJiMmc8SXlFioynhAIHpXUq00ITlmQlFIlOKxZrWULFqkSxKTob_nbOvm6UD2JtN67tKwUFRhPKezF9CoZU6frNTmnROdNItxVAxE6gGASKXqDYCRTQM_wXU5qw1xCcNPW_JB1I37e0z8r9bPob-gJsPYde
CitedBy_id	crossref_primary_10_1007_s10013_024_00721_y crossref_primary_10_1007_s10957_024_02400_x crossref_primary_10_1080_02331934_2020_1836637 crossref_primary_10_1007_s11117_024_01103_x crossref_primary_10_1007_s40306_023_00522_4 crossref_primary_10_1007_s11228_021_00601_4 crossref_primary_10_1007_s40314_025_03151_9 crossref_primary_10_1080_02331934_2019_1687697
Cites_doi	10.1142/5021 10.1007/978-1-4612-1394-9 10.1007/s10957-016-0900-7 10.1007/s11228-017-0426-7 10.1287/moor.21.3.555 10.1006/jfan.1993.1141 10.1080/00036811.2014.890710 10.1007/s10107-007-0120-x 10.1515/9781400873173 10.1016/0362-546X(94)00221-3 10.1090/S0002-9939-1965-0178103-8 10.1016/S0924-6509(09)70252-1 10.1007/978-1-4614-4538-8 10.1007/3-540-31246-3 10.1007/BF01027108 10.1137/0804038 10.1007/BF01100690 10.1007/978-1-4757-6019-4_13
ContentType	Journal Article
Copyright	Springer Science+Business Media, LLC, part of Springer Nature 2018 Journal of Optimization Theory and Applications is a copyright of Springer, (2018). All Rights Reserved.
Copyright_xml	– notice: Springer Science+Business Media, LLC, part of Springer Nature 2018 – notice: Journal of Optimization Theory and Applications is a copyright of Springer, (2018). All Rights Reserved.
DBID	AAYXX CITATION 7SC 7TB 8FD FR3 JQ2 KR7 L7M L~C L~D
DOI	10.1007/s10957-018-1431-1
DatabaseName	CrossRef Computer and Information Systems Abstracts Mechanical & Transportation Engineering Abstracts Technology Research Database Engineering Research Database ProQuest Computer Science Collection Civil Engineering Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional
DatabaseTitle	CrossRef Civil Engineering Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Mechanical & Transportation Engineering Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Engineering Research Database Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional
DatabaseTitleList	Civil Engineering Abstracts
DeliveryMethod	fulltext_linktorsrc
Discipline	Engineering Mathematics
EISSN	1573-2878
EndPage	143
ExternalDocumentID	10_1007_s10957_018_1431_1
GroupedDBID	-52 -5D -5G -BR -EM -~C -~X .4S .86 .DC .VR 06D 0R~ 0VY 199 1N0 203 29L 2J2 2JN 2JY 2KG 2KM 2LR 2~H 30V 4.4 406 408 409 40D 40E 5GY 5VS 67Z 6NX 78A 7WY 88I 8AO 8FE 8FG 8FL 8G5 8TC 8UJ 95- 95. 95~ 96X AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYZH ABAKF ABBBX ABBXA ABDZT ABECU ABFTV ABHLI ABHQN ABJCF ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABSXP ABTEG ABTHY ABTKH ABTMW ABUWG ABWNU ABXPI ACAOD ACDTI ACGFS ACGOD ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACZOJ ADHHG ADHIR ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEFQL AEGAL AEGNC AEJHL AEJRE AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFKRA AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARAPS ARCSS ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN AZQEC B-. BA0 BAPOH BDATZ BENPR BEZIV BGLVJ BGNMA BPHCQ BSONS CCPQU CS3 CSCUP DDRTE DL5 DNIVK DPUIP DU5 DWQXO EBLON EBS EDO EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRNLG FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNUQQ GNWQR GQ6 GQ7 GQ8 GROUPED_ABI_INFORM_COMPLETE GROUPED_ABI_INFORM_RESEARCH GUQSH GXS HCIFZ HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF I-F I09 IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ K60 K6V K6~ K7- KDC KOV L6V LAK LLZTM M0C M2O M2P M4Y M7S MA- N9A NB0 NPVJJ NQJWS NU0 O93 O9G O9I O9J OAM P19 P2P P62 P9R PF0 PQBIZ PQBZA PQQKQ PROAC PT4 PT5 PTHSS Q2X QOK QOS R89 R9I RHV RNS ROL RPX RSV S16 S27 S3B SAP SDD SDH SDM SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 TN5 TSG TSK TSV TUC TUS TWZ U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WH7 WK8 YLTOR YQT Z45 Z7R Z7S Z7U Z7X Z7Y Z7Z Z81 Z83 Z86 Z88 Z8M Z8N Z8R Z8S Z8T Z8U Z8W Z92 ZMTXR ~EX -Y2 1SB 2.D 28- 2P1 2VQ 5QI AAAVM AAPKM AARHV AAYTO AAYXX ABBRH ABDBE ABDPE ABFSG ABQSL ABRTQ ABULA ACBXY ACSTC ADHKG ADXHL AEBTG AEFIE AEKMD AEZWR AFDZB AFEXP AFFHD AFGCZ AFHIU AFOHR AGGDS AGQPQ AHPBZ AHWEU AI. AIXLP AJBLW AMVHM ATHPR AYFIA BBWZM CAG CITATION COF H13 H~9 KOW N2Q NDZJH OVD PHGZM PHGZT PQGLB R4E RNI RZC RZE RZK S1Z S26 S28 SCLPG T16 TEORI VH1 VOH ZCG ZWQNP ZY4 7SC 7TB 8FD FR3 JQ2 KR7 L7M L~C L~D
ID	FETCH-LOGICAL-c316t-f1341bb34901ccd3a937567d0b87602171eff6a6bf0358c1b5f6d34fac1d3d5e3
IEDL.DBID	RSV
ISICitedReferencesCount	9
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000460754800006&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	0022-3239
IngestDate	Tue Nov 04 23:01:53 EST 2025 Tue Nov 18 20:33:33 EST 2025 Sat Nov 29 06:02:29 EST 2025 Fri Feb 21 02:34:14 EST 2025
IsPeerReviewed	true
IsScholarly	true
Issue	1
Keywords	90C31 Optimal value function Subdifferentials 49J53 90C25 Conjugate function Parametric convex programming 49Q12 Normal directions
Language	English
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c316t-f1341bb34901ccd3a937567d0b87602171eff6a6bf0358c1b5f6d34fac1d3d5e3
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
PQID	2132527095
PQPubID	48247
PageCount	18
ParticipantIDs	proquest_journals_2132527095 crossref_primary_10_1007_s10957_018_1431_1 crossref_citationtrail_10_1007_s10957_018_1431_1 springer_journals_10_1007_s10957_018_1431_1
PublicationCentury	2000
PublicationDate	2019-04-01
PublicationDateYYYYMMDD	2019-04-01
PublicationDate_xml	– month: 04 year: 2019 text: 2019-04-01 day: 01
PublicationDecade	2010
PublicationPlace	New York
PublicationPlace_xml	– name: New York
PublicationTitle	Journal of optimization theory and applications
PublicationTitleAbbrev	J Optim Theory Appl
PublicationYear	2019
Publisher	Springer US Springer Nature B.V
Publisher_xml	– name: Springer US – name: Springer Nature B.V
References	Seeger (CR17) 1994; 2 Mordukhovich (CR3) 2006 Penot (CR6) 2013 Hiriart-Urruty, Lemaréchal (CR14) 1993 Ioffe, Tihomirov (CR19) 1979 Mordukhovich, Nam, Rector, Tran (CR4) 2017; 25 Mordukhovich, Nam, Yen (CR5) 2009; 116 An, Yen (CR1) 2015; 94 Volle (CR10) 1994; 5 CR12 CR11 Brøndsted, Rockafellar (CR9) 1965; 16 Attouch, Brezis, Barraso (CR20) 1986 An, Yao (CR2) 2016; 170 Hiriart-Urruty, Phelps (CR15) 1993; 118 Rockafellar (CR7) 1970 Hiriart-Urruty, Moussaoui, Seeger, Volle (CR13) 1995; 24 Moussaoui, Seeger (CR16) 1994; 4 Seeger (CR18) 1996; 21 Zănlinescu (CR8) 2002 Bonnans, Shapiro (CR21) 2000 1431_CR11 1431_CR12 BS Mordukhovich (1431_CR5) 2009; 116 RT Rockafellar (1431_CR7) 1970 J-P Penot (1431_CR6) 2013 A Seeger (1431_CR18) 1996; 21 BS Mordukhovich (1431_CR4) 2017; 25 A Brøndsted (1431_CR9) 1965; 16 M Moussaoui (1431_CR16) 1994; 4 A Seeger (1431_CR17) 1994; 2 AD Ioffe (1431_CR19) 1979 H Attouch (1431_CR20) 1986 J-B Hiriart-Urruty (1431_CR13) 1995; 24 M Volle (1431_CR10) 1994; 5 DTV An (1431_CR1) 2015; 94 C Zănlinescu (1431_CR8) 2002 J-B Hiriart-Urruty (1431_CR14) 1993 J-B Hiriart-Urruty (1431_CR15) 1993; 118 DTV An (1431_CR2) 2016; 170 BS Mordukhovich (1431_CR3) 2006 JF Bonnans (1431_CR21) 2000
References_xml	– year: 2002 ident: CR8 publication-title: Convex Analysis in General Vector Spaces doi: 10.1142/5021 – year: 2000 ident: CR21 publication-title: Perturbation Analysis of Optimization Problems doi: 10.1007/978-1-4612-1394-9 – volume: 170 start-page: 28 year: 2016 end-page: 42 ident: CR2 article-title: Further results on differential stability of convex optimization problems publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-016-0900-7 – volume: 25 start-page: 731 year: 2017 end-page: 755 ident: CR4 article-title: Variational geometric approach to generalized differential and conjugate calculi in convex analysis publication-title: Set Valued Var. Anal. doi: 10.1007/s11228-017-0426-7 – volume: 21 start-page: 555 year: 1996 end-page: 575 ident: CR18 article-title: Subgradients of optimal-value functions in dynamic programming: the case of convex systems without optimal paths publication-title: Math. Oper. Res. doi: 10.1287/moor.21.3.555 – volume: 118 start-page: 154 year: 1993 end-page: 166 ident: CR15 article-title: Subdifferential calculus using -subdifferentials publication-title: J. Funct. Anal. doi: 10.1006/jfan.1993.1141 – volume: 94 start-page: 108 year: 2015 end-page: 128 ident: CR1 article-title: Differential stability of convex optimization problems under inclusion constraints publication-title: Appl. Anal. doi: 10.1080/00036811.2014.890710 – volume: 116 start-page: 369 year: 2009 end-page: 396 ident: CR5 article-title: Subgradients of marginal functions in parametric mathematical programming publication-title: Math. Program. Ser. B doi: 10.1007/s10107-007-0120-x – year: 1970 ident: CR7 publication-title: Convex Analysis doi: 10.1515/9781400873173 – volume: 24 start-page: 1727 year: 1995 end-page: 1754 ident: CR13 article-title: Subdifferential calculus without qualification conditions, using approximate subdifferentials: a survey publication-title: Nonlinear Anal. doi: 10.1016/0362-546X(94)00221-3 – volume: 16 start-page: 605 year: 1965 end-page: 611 ident: CR9 article-title: On the subdifferentiability of convex functions publication-title: Proc. Am. Math. Soc. doi: 10.1090/S0002-9939-1965-0178103-8 – start-page: 125 year: 1986 end-page: 133 ident: CR20 article-title: Duality for the sum of convex functions in general Banach spaces publication-title: Aspects of Mathematics and Its Applications doi: 10.1016/S0924-6509(09)70252-1 – year: 2013 ident: CR6 publication-title: Calculus Without Derivatives. Graduate Texts in Mathematics doi: 10.1007/978-1-4614-4538-8 – ident: CR12 – year: 1979 ident: CR19 publication-title: Theory of Extremal Problems – ident: CR11 – year: 2006 ident: CR3 publication-title: Variational Analysis and Generalized Differentiation, Volume I: Basic Theory, Volume II: Applications doi: 10.1007/3-540-31246-3 – volume: 2 start-page: 307 year: 1994 end-page: 325 ident: CR17 article-title: Approximate Euler-Lagrange inclusion, approximate transversality condition, and sensitivity analysis of convex parametric problems of calculus of variations publication-title: Set Valued Anal. doi: 10.1007/BF01027108 – volume: 4 start-page: 659 year: 1994 end-page: 675 ident: CR16 article-title: Sensitivity analysis of optimal value functions of convex parametric programs with possibly empty solution sets publication-title: SIAM J. Optim. doi: 10.1137/0804038 – volume: 5 start-page: 131 year: 1994 end-page: 157 ident: CR10 article-title: Calculus rules for global approximate minima and applications to approximate subdifferential calculus publication-title: J. Glob. Optim. doi: 10.1007/BF01100690 – year: 1993 ident: CR14 publication-title: Convex Analysis and Minimization Aalgorithms. II. Advanced Theory and Bundle Methods. Grundlehren Math. Wiss – volume-title: Theory of Extremal Problems year: 1979 ident: 1431_CR19 – ident: 1431_CR12 doi: 10.1007/978-1-4757-6019-4_13 – volume: 21 start-page: 555 year: 1996 ident: 1431_CR18 publication-title: Math. Oper. Res. doi: 10.1287/moor.21.3.555 – volume-title: Convex Analysis year: 1970 ident: 1431_CR7 doi: 10.1515/9781400873173 – volume-title: Calculus Without Derivatives. Graduate Texts in Mathematics year: 2013 ident: 1431_CR6 doi: 10.1007/978-1-4614-4538-8 – volume-title: Convex Analysis and Minimization Aalgorithms. II. Advanced Theory and Bundle Methods. Grundlehren Math. Wiss year: 1993 ident: 1431_CR14 – volume: 4 start-page: 659 year: 1994 ident: 1431_CR16 publication-title: SIAM J. Optim. doi: 10.1137/0804038 – volume: 118 start-page: 154 year: 1993 ident: 1431_CR15 publication-title: J. Funct. Anal. doi: 10.1006/jfan.1993.1141 – ident: 1431_CR11 – volume-title: Perturbation Analysis of Optimization Problems year: 2000 ident: 1431_CR21 doi: 10.1007/978-1-4612-1394-9 – start-page: 125 volume-title: Aspects of Mathematics and Its Applications year: 1986 ident: 1431_CR20 doi: 10.1016/S0924-6509(09)70252-1 – volume: 24 start-page: 1727 year: 1995 ident: 1431_CR13 publication-title: Nonlinear Anal. doi: 10.1016/0362-546X(94)00221-3 – volume-title: Variational Analysis and Generalized Differentiation, Volume I: Basic Theory, Volume II: Applications year: 2006 ident: 1431_CR3 doi: 10.1007/3-540-31246-3 – volume: 116 start-page: 369 year: 2009 ident: 1431_CR5 publication-title: Math. Program. Ser. B doi: 10.1007/s10107-007-0120-x – volume: 94 start-page: 108 year: 2015 ident: 1431_CR1 publication-title: Appl. Anal. doi: 10.1080/00036811.2014.890710 – volume: 170 start-page: 28 year: 2016 ident: 1431_CR2 publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-016-0900-7 – volume: 5 start-page: 131 year: 1994 ident: 1431_CR10 publication-title: J. Glob. Optim. doi: 10.1007/BF01100690 – volume: 16 start-page: 605 year: 1965 ident: 1431_CR9 publication-title: Proc. Am. Math. Soc. doi: 10.1090/S0002-9939-1965-0178103-8 – volume: 2 start-page: 307 year: 1994 ident: 1431_CR17 publication-title: Set Valued Anal. doi: 10.1007/BF01027108 – volume: 25 start-page: 731 year: 2017 ident: 1431_CR4 publication-title: Set Valued Var. Anal. doi: 10.1007/s11228-017-0426-7 – volume-title: Convex Analysis in General Vector Spaces year: 2002 ident: 1431_CR8 doi: 10.1142/5021
SSID	ssj0009874
Score	2.2782588
Snippet	This paper studies differential stability of infinite-dimensional convex optimization problems, whose solution sets may be empty. By using suitable sum rules...
SourceID	proquest crossref springer
SourceType	Aggregation Database Enrichment Source Index Database Publisher
StartPage	126
SubjectTerms	Applications of Mathematics Calculus of Variations and Optimal Control; Optimization Computational geometry Convex analysis Convexity Dimensional stability Engineering Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Sum rules Theory of Computation
Title	Differential Stability of Convex Optimization Problems with Possibly Empty Solution Sets
URI	https://link.springer.com/article/10.1007/s10957-018-1431-1 https://www.proquest.com/docview/2132527095
Volume	181
WOSCitedRecordID	wos000460754800006&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: 1573-2878 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0009874 issn: 0022-3239 databaseCode: RSV dateStart: 19970101 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/eLvHCXMwnV3NS8MwFA8yPejBb3E6JQdPSqBtkjY9ytzwoHM4HbuVNk1A2BdrFfff-9I22xQV9FjyQXnJe-_3kpffQ-gioFQFjvKI5IEmTDBK4kCERNM0jHmoElZUa-jfBZ2OGAzCbvWOO7PZ7vZKsrDUK4_dQm7SJCHqAa9HIORZB28nTL2Gx15_ybQrLPWyR6hHQ3uV-d0Un53REmF-uRQtfE17519_uYu2K2iJr8u9sIfW1Hgfba0QDsLX_YKlNTtAg5uqOgpo-RAD7CwSZed4onHTJKO_4wcwKKPqpSbulrVnMmzObnF3YrRpOMet0RTG2OM13FN5doie262n5i2pKi0QSV0_J9rQuiUJZYAOpExpDKCF-0HqJGAsTdTiKq392E-0Q7mQbsK1n1KmY-mmNOWKHqHaeDJWxwgnALA87YPvZS7TqTLxlJDcUa5Ifcl4HTlW5JGsaMhNNYxhtCRQNiKMQISREWHk1tHlYsi05OD4rXPDrmNUqWMWeRBzcy-ArnV0Zddt2fzjZCd_6n2KNgFOhWVeTwPV8tmrOkMb8i1_yWbnxS79AC7l4Lg
linkProvider	Springer Nature
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LSwMxEA5SBfXgW6xWzcGTEtjdJPs4Sm2p2NZia-lt2c0mIPRFdxX7753so62igh6XPFgmmZlvksk3CF05lErHkBYR3FGEuYySwHE9omjkBdyTIUurNfSbTrvtDgZeJ3_HHRfZ7sWVZGqpVx67eVynSULUA16PQMizzsBhacL8p25_ybTrFtTLFqEW9YqrzO-m-OyMlgjzy6Vo6mvqu__6yz20k0NLfJvthX20JscHaHuFcBC-WguW1vgQDe7y6iig5UMMsDNNlJ3jicJVnYz-jh_BoIzyl5q4k9WeibE-u8Wdidam4RzXRlMYUxyv4a5M4iP0XK_1qg2SV1oggpp2QpSmdQtDygAdCBHRAEALt53ICMFY6qjFlErZgR0qg3JXmCFXdkSZCoQZ0YhLeoxK48lYniAcAsCylA2-l5lMRVLHU67ghjTdyBaMl5FRiNwXOQ25roYx9JcEylqEPojQ1yL0zTK6XgyZZhwcv3WuFOvo5-oY-xbE3NxyoGsZ3RTrtmz-cbLTP_W-RJuNXqvpN-_bD2doC6CVl-X4VFApmb3Kc7Qh3pKXeHaR7tgPv-DjnA
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LSwMxEA5SRfTgW6xWzcGTErq7SfZxlD5QrLVQLb0tu3mA0BfdVey_d9LdtVVUEI9LJmGZZDLfJJNvELrwKFWepRwiuKcJ8xklkecHRFMZRDxQMZtXa-i1vHbb7_eDTl7nNCmy3YsryexNg2FpGqXVidTVpYdvATcpkxABgQckEP6sMpNHb8L1bm_BuusXNMwOoQ4NimvN74b47JgWaPPLBenc7zS3__3HO2grh5z4Olsju2hFjfbQ5hIRIXzdf7C3JvuoX8-rpoD1DzDA0XkC7QyPNa6ZJPU3_AAbzTB_wYk7WU2aBJszXdwZGysbzHBjOIE-xbEb7qo0OUBPzcZj7YbkFRiIoLabEm3o3uKYMkANQkgaAZjhrietGDZRE83YSms3cmNtUe4LO-balZTpSNiSSq7oISqNxiN1hHAMwMvRLvhkZjMtlYmzfMEtZfvSFYyXkVWoPxQ5PbmpkjEIF8TKRoUhqDA0KgztMrr86DLJuDl-E64UcxrmZpqEDsTi3PFAtIyuijlcNP842PGfpM_ReqfeDFu37bsTtAGIK8hSfyqolE5f1ClaE6_pczI9my_ed4C77IA
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=Differential+Stability+of+Convex+Optimization+Problems+with+Possibly+Empty+Solution+Sets&rft.jtitle=Journal+of+optimization+theory+and+applications&rft.au=An%2C+Duong+Thi+Viet&rft.au=Yao%2C+Jen-Chih&rft.date=2019-04-01&rft.issn=0022-3239&rft.eissn=1573-2878&rft.volume=181&rft.issue=1&rft.spage=126&rft.epage=143&rft_id=info:doi/10.1007%2Fs10957-018-1431-1&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s10957_018_1431_1
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0022-3239&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0022-3239&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0022-3239&client=summon