Second-order variational analysis and characterizations of tilt-stable optimal solutions in infinite-dimensional spaces
The paper is devoted to developing second-order tools of variational analysis and their applications to characterizing tilt-stable local minimizers of constrained optimization problems infinite-dimensional spaces with many results new also in finite-dimensional settings. The importance of tilt stabi...
Uložené v:
| Vydané v: | Nonlinear analysis Ročník 86; s. 159 - 180 |
|---|---|
| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Elsevier Ltd
01.07.2013
|
| Predmet: | |
| ISSN: | 0362-546X, 1873-5215 |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Abstract | The paper is devoted to developing second-order tools of variational analysis and their applications to characterizing tilt-stable local minimizers of constrained optimization problems infinite-dimensional spaces with many results new also in finite-dimensional settings. The importance of tilt stability has been well recognized from both theoretical and numerical aspects of optimization. Based on second-order generalized differentiation, we obtain qualitative and quantitative characterizations of tilt stability in general frameworks of constrained optimization and establish its relationships with strong metric regularity of subgradient mappings and uniform second-order growth. The results obtained are applied to deriving new necessary and sufficient conditions for tilt-stable minimizers in problems of nonlinear programming with twice continuously differentiable data in Hilbert spaces. |
|---|---|
| AbstractList | The paper is devoted to developing second-order tools of variational analysis and their applications to characterizing tilt-stable local minimizers of constrained optimization problems infinite-dimensional spaces with many results new also in finite-dimensional settings. The importance of tilt stability has been well recognized from both theoretical and numerical aspects of optimization. Based on second-order generalized differentiation, we obtain qualitative and quantitative characterizations of tilt stability in general frameworks of constrained optimization and establish its relationships with strong metric regularity of subgradient mappings and uniform second-order growth. The results obtained are applied to deriving new necessary and sufficient conditions for tilt-stable minimizers in problems of nonlinear programming with twice continuously differentiable data in Hilbert spaces. |
| Author | Nghia, T.T.A. Mordukhovich, B.S. |
| Author_xml | – sequence: 1 givenname: B.S. surname: Mordukhovich fullname: Mordukhovich, B.S. email: boris@math.wayne.edu organization: Department of Mathematics, Wayne State University, Detroit, MI 48202, USA – sequence: 2 givenname: T.T.A. surname: Nghia fullname: Nghia, T.T.A. email: nghia@math.wayne.edu organization: Department of Mathematics, Wayne State University, Detroit, MI 48202, USA |
| BookMark | eNqFkc2LFDEQxYOs4OzHfY999NJjpdNJd3uTxS9Y8KAL3kImqcYaepIxlVlZ_3qz254EFR5VgbzfO7w6F2cxRRTiWsJWgjSv9tvoth1ItYUq2T8TGzkOqtWd1GdiA8p0re7N1xfinHkPAHJQZiN-fEafYmhTDpibe5fJFUrRLY2r44GJ6yM0_pvLzhfM9PPpn5s0N4WW0nJxuwWbdCx0qBSn5bQaKFbNFKlgG-iAkddcPjqPfCmez25hvPq9L8Tdu7dfbj60t5_ef7x5c9t6ZaC0fvBhNLOTTuuA8xD0MDkFenSod2NVP05GzdOkPMrJdAp2ZvY9jjiEbvSgLsTLNfeY0_cTcrEHYo_L4iKmE1upwaiaIvX_rf2gddcBqGo1q9XnxJxxtp7KUzElO1qsBPt4FLu30dnHo1iokn0F4Q_wmGtv-eFfyOsVwVrTPWG27Amjx0AZfbEh0d_hX6mYqG8 |
| CitedBy_id | crossref_primary_10_1137_17M113424X crossref_primary_10_1007_s10013_019_00339_5 crossref_primary_10_1007_s11228_018_0474_7 crossref_primary_10_1007_s00245_017_9432_2 crossref_primary_10_1007_s10957_024_02413_6 crossref_primary_10_1007_s11228_024_00716_4 crossref_primary_10_1155_2014_596582 crossref_primary_10_1016_j_na_2014_10_013 crossref_primary_10_1137_22M1519250 crossref_primary_10_1287_moor_2014_0669 crossref_primary_10_1137_130928637 crossref_primary_10_1080_02331934_2016_1208656 crossref_primary_10_1137_23M1604667 crossref_primary_10_1287_moor_2017_0889 crossref_primary_10_1016_j_na_2015_05_030 crossref_primary_10_1515_jaa_2019_0006 crossref_primary_10_12677_AAM_2019_81014 crossref_primary_10_1007_s10013_025_00739_w crossref_primary_10_1007_s10957_021_01890_3 crossref_primary_10_1016_j_na_2015_02_020 crossref_primary_10_1137_23M1627237 crossref_primary_10_1007_s11750_015_0370_3 crossref_primary_10_1080_02331934_2020_1751159 crossref_primary_10_1080_02331934_2014_951043 crossref_primary_10_1137_130906878 crossref_primary_10_1186_s13660_016_0977_4 crossref_primary_10_1080_01630563_2014_895747 crossref_primary_10_1017_S1446788719000090 crossref_primary_10_1137_16M1086741 crossref_primary_10_1007_s10957_016_0952_8 crossref_primary_10_1007_s11228_016_0366_7 crossref_primary_10_1007_s11784_015_0220_9 crossref_primary_10_1007_s10898_021_01100_4 crossref_primary_10_1137_140959845 crossref_primary_10_1137_17M1153224 crossref_primary_10_1137_18M1213117 crossref_primary_10_1007_s10898_015_0271_x |
| Cites_doi | 10.1137/120876551 10.1007/s10107-012-0553-8 10.1023/B:SVAN.0000023403.87092.a2 10.1287/moor.5.1.43 10.1137/S1052623495284029 10.1090/S0002-9947-96-01544-9 10.1023/A:1008746317549 10.1137/S1052623498348274 10.1137/120887722 10.1016/j.na.2010.08.029 10.1137/S1052623496309296 10.1016/j.jmaa.2004.06.003 10.1137/110852528 10.1016/j.na.2011.08.014 10.1137/110852103 |
| ContentType | Journal Article |
| Copyright | 2013 Elsevier Ltd |
| Copyright_xml | – notice: 2013 Elsevier Ltd |
| DBID | AAYXX CITATION 7SC 7TB 8FD FR3 JQ2 KR7 L7M L~C L~D |
| DOI | 10.1016/j.na.2013.03.014 |
| 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 Civil Engineering Abstracts |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences Engineering Mathematics |
| EISSN | 1873-5215 |
| EndPage | 180 |
| ExternalDocumentID | 10_1016_j_na_2013_03_014 S0362546X13001041 |
| GrantInformation_xml | – fundername: National Science Foundation grantid: DMS-1007132 |
| GroupedDBID | --K --M -~X .~1 0R~ 123 1B1 1RT 1~. 1~5 29N 4.4 457 4G. 5VS 7-5 71M 8P~ 9JN AABNK AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO ABAOU ABEFU ABFNM ABLJU ABMAC ABXDB ABYKQ ACAZW ACDAQ ACGFS ACIWK ACNNM ACRLP ADBBV ADEZE ADGUI ADIYS ADMUD ADTZH AEBSH AECPX AEKER AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHJVU AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR ASPBG AVWKF AXJTR AZFZN BJAXD BKOJK BLXMC CS3 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 GBLVA HMJ HVGLF HZ~ IHE J1W JJJVA KOM M26 M41 MHUIS MO0 MVM N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. Q38 R2- RIG ROL RPZ SDF SDG SDP SES SEW SME SPC SPCBC SST SSW SSZ T5K TN5 WUQ XPP YQT ZMT ~G- 9DU AATTM AAXKI AAYWO AAYXX ABJNI ABWVN ACLOT ACRPL ADNMO AEIPS AFJKZ AGQPQ AIIUN ANKPU APXCP CITATION EFKBS ~HD 7SC 7TB 8FD FR3 JQ2 KR7 L7M L~C L~D |
| ID | FETCH-LOGICAL-c360t-c7cd86fa1a55def7d579a3058ae5b85b848963f993ce196230b6fc4e8e7d28c03 |
| ISICitedReferencesCount | 41 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000318907300013&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0362-546X |
| IngestDate | Sun Sep 28 12:22:50 EDT 2025 Sun Sep 28 09:13:31 EDT 2025 Sat Nov 29 02:58:07 EST 2025 Tue Nov 18 21:49:07 EST 2025 Fri Feb 23 02:29:48 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | Variational analysis and optimization Second-order growth Lipschitzian stability Strong metric regularity First-order and second-order generalized differentiation |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c360t-c7cd86fa1a55def7d579a3058ae5b85b848963f993ce196230b6fc4e8e7d28c03 |
| Notes | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
| PQID | 1475522003 |
| PQPubID | 23500 |
| PageCount | 22 |
| ParticipantIDs | proquest_miscellaneous_1506384815 proquest_miscellaneous_1475522003 crossref_citationtrail_10_1016_j_na_2013_03_014 crossref_primary_10_1016_j_na_2013_03_014 elsevier_sciencedirect_doi_10_1016_j_na_2013_03_014 |
| PublicationCentury | 2000 |
| PublicationDate | 2013-07-01 |
| PublicationDateYYYYMMDD | 2013-07-01 |
| PublicationDate_xml | – month: 07 year: 2013 text: 2013-07-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationTitle | Nonlinear analysis |
| PublicationYear | 2013 |
| Publisher | Elsevier Ltd |
| Publisher_xml | – name: Elsevier Ltd |
| References | R. Henrion, A.Y. Kruger, J.V. Outrata, Some remarks on stability of generalized equations, J. Optim. Theory Appl., in press B.S. Mordukhovich, R.T. Rockafellar, M.E. Sarabi, Characterizations of full stability in constrained optimization, SIAM J. Optim. (2013) (in press). Robinson (br000120) 1980; 5 Borwein, Zhu (br000075) 2005 Bauschke, Combettes (br000065) 2011 Chieu, Huy (br000140) 2011; 74 Henrion, Outrata, Surowiec (br000110) 2012; 136 Schirotzek (br000080) 2007 Penot (br000145) 1998; 6 Zălinescu (br000070) 2002 Eberhard, Wenczel (br000015) 2012; 75 Drusvyatskiy, Lewis (br000010) 2013; 23 Poliquin, Rockafellar (br000005) 1998; 8 Levy, Poliquin, Rockafellar (br000045) 2000; 10 B.S. Mordukhovich, T.T.A. Nghia, Second-order characterizations of tilt stability with applications to nonlinear programming, 2013. Preprint. Ito, Kunisch (br000125) 2008 Poliquin, Rockafellar (br000090) 1996; 348 Lewis, Zhang (br000020) 2013; 23 Bernard, Thibault (br000100) 2005; 303 Mordukhovich, Rockafellar (br000030) 2012; 22 Dontchev, Rockafellar (br000085) 2009 Mordukhovich (br000055) 2006 . Mordukhovich (br000050) 1992; vol. 58 B.S. Mordukhovich, J.V. Outrata, Tilt stability in nonlinear programming under Mangasarian–Fromovitz constraint qualification, Kybernetika (in press). Bernard, Thibault (br000095) 2004; 12 Aragón Artacho, Geoffroy (br000115) 2008; 15 Rockafellar, Wets (br000060) 1998 Dontchev, Rockafellar (br000135) 1996; 6 Bonnans, Shapiro (br000040) 2000 Mordukhovich (10.1016/j.na.2013.03.014_br000055) 2006 Henrion (10.1016/j.na.2013.03.014_br000110) 2012; 136 Poliquin (10.1016/j.na.2013.03.014_br000005) 1998; 8 Mordukhovich (10.1016/j.na.2013.03.014_br000030) 2012; 22 10.1016/j.na.2013.03.014_br000035 Dontchev (10.1016/j.na.2013.03.014_br000085) 2009 10.1016/j.na.2013.03.014_br000130 Bauschke (10.1016/j.na.2013.03.014_br000065) 2011 Ito (10.1016/j.na.2013.03.014_br000125) 2008 Aragón Artacho (10.1016/j.na.2013.03.014_br000115) 2008; 15 Dontchev (10.1016/j.na.2013.03.014_br000135) 1996; 6 Borwein (10.1016/j.na.2013.03.014_br000075) 2005 Rockafellar (10.1016/j.na.2013.03.014_br000060) 1998 Penot (10.1016/j.na.2013.03.014_br000145) 1998; 6 Schirotzek (10.1016/j.na.2013.03.014_br000080) 2007 Bernard (10.1016/j.na.2013.03.014_br000100) 2005; 303 Eberhard (10.1016/j.na.2013.03.014_br000015) 2012; 75 Poliquin (10.1016/j.na.2013.03.014_br000090) 1996; 348 10.1016/j.na.2013.03.014_br000105 Bernard (10.1016/j.na.2013.03.014_br000095) 2004; 12 10.1016/j.na.2013.03.014_br000025 Lewis (10.1016/j.na.2013.03.014_br000020) 2013; 23 Bonnans (10.1016/j.na.2013.03.014_br000040) 2000 Robinson (10.1016/j.na.2013.03.014_br000120) 1980; 5 Levy (10.1016/j.na.2013.03.014_br000045) 2000; 10 Mordukhovich (10.1016/j.na.2013.03.014_br000050) 1992; vol. 58 Chieu (10.1016/j.na.2013.03.014_br000140) 2011; 74 Drusvyatskiy (10.1016/j.na.2013.03.014_br000010) 2013; 23 Zălinescu (10.1016/j.na.2013.03.014_br000070) 2002 |
| References_xml | – volume: 23 start-page: 256 year: 2013 end-page: 267 ident: br000010 article-title: Tilt stability, uniform quadratic growth, and strong metric regularity of the subdifferential publication-title: SIAM J. Optim. – reference: B.S. Mordukhovich, T.T.A. Nghia, Second-order characterizations of tilt stability with applications to nonlinear programming, 2013. Preprint. – year: 2000 ident: br000040 article-title: Perturbation Analysis of Optimization Problems – reference: B.S. Mordukhovich, J.V. Outrata, Tilt stability in nonlinear programming under Mangasarian–Fromovitz constraint qualification, Kybernetika (in press). – year: 1998 ident: br000060 article-title: Variational Analysis – year: 2002 ident: br000070 article-title: Convex Analysis in General Vector Spaces – year: 2011 ident: br000065 article-title: Convex Analysis and Monotone Operator Theory in Hilbert Spaces – reference: ). – year: 2007 ident: br000080 article-title: Nonsmooth Analysis – volume: vol. 58 start-page: 32 year: 1992 end-page: 46 ident: br000050 article-title: Sensitivity analysis in nonsmooth optimization publication-title: Theoretical Aspects of Industrial Design – volume: 348 start-page: 1805 year: 1996 end-page: 1838 ident: br000090 article-title: Prox-regular functions in variational analysis publication-title: Trans. Amer. Math. Soc. – reference: B.S. Mordukhovich, R.T. Rockafellar, M.E. Sarabi, Characterizations of full stability in constrained optimization, SIAM J. Optim. (2013) (in press). – reference: R. Henrion, A.Y. Kruger, J.V. Outrata, Some remarks on stability of generalized equations, J. Optim. Theory Appl., in press ( – volume: 8 start-page: 287 year: 1998 end-page: 299 ident: br000005 article-title: Tilt stability of a local minimum publication-title: SIAM J. Optim. – volume: 5 start-page: 43 year: 1980 end-page: 62 ident: br000120 article-title: Strongly regular generalized equations publication-title: Math. Oper. Res. – year: 2008 ident: br000125 article-title: Lagrange Multiplier Approach to Variational Problems and Applications – volume: 10 start-page: 580 year: 2000 end-page: 604 ident: br000045 article-title: Stability of locally optimal solutions publication-title: SIAM J. Optim. – volume: 12 start-page: 25 year: 2004 end-page: 47 ident: br000095 article-title: Prox-regular functions and sets in Banach spaces publication-title: Set-Valued Anal. – volume: 75 start-page: 1260 year: 2012 end-page: 1281 ident: br000015 article-title: A study of tilt-stable optimality and sufficient conditions publication-title: Nonlinear Anal. – year: 2009 ident: br000085 article-title: Implicit Functions and Solution Mappings. A View from Variational Analysis – volume: 15 start-page: 365 year: 2008 end-page: 380 ident: br000115 article-title: Charaterizations of metric regularity of subdifferentials publication-title: J. Convex Anal. – year: 2006 ident: br000055 article-title: Variational Analysis and Generalized Differentiation, I: Basic Theory, II: Applications – volume: 6 start-page: 363 year: 1998 end-page: 380 ident: br000145 article-title: Compactness properties, openness criteria and coderivatives publication-title: Set-Valued Anal. – volume: 74 start-page: 154 year: 2011 end-page: 160 ident: br000140 article-title: Second-order subdifferentials and convexity of real-valued functions publication-title: Nonlinear Anal. – volume: 303 start-page: 1 year: 2005 end-page: 14 ident: br000100 article-title: Prox-regular functions in Hilbert spaces publication-title: J. Math. Anal. Appl. – year: 2005 ident: br000075 article-title: Techniques of Variational Analysis – volume: 23 start-page: 74 year: 2013 end-page: 94 ident: br000020 article-title: Partial smoothness, tilt stability, and generalized Hessians publication-title: SIAM J. Optim. – volume: 136 start-page: 111 year: 2012 end-page: 131 ident: br000110 article-title: On regular coderivatives in parametric equilibria with non-unique multipliers publication-title: Math. Program. – volume: 6 start-page: 1087 year: 1996 end-page: 1105 ident: br000135 article-title: Characterizations of strong regularity for variational inequalities over polyhedral convex sets publication-title: SIAM J. Optim. – volume: 22 start-page: 953 year: 2012 end-page: 986 ident: br000030 article-title: Second-order subdifferential calculus with applications to tilt stability in optimization publication-title: SIAM J. Optim. – volume: 23 start-page: 256 year: 2013 ident: 10.1016/j.na.2013.03.014_br000010 article-title: Tilt stability, uniform quadratic growth, and strong metric regularity of the subdifferential publication-title: SIAM J. Optim. doi: 10.1137/120876551 – year: 2002 ident: 10.1016/j.na.2013.03.014_br000070 – volume: 136 start-page: 111 year: 2012 ident: 10.1016/j.na.2013.03.014_br000110 article-title: On regular coderivatives in parametric equilibria with non-unique multipliers publication-title: Math. Program. doi: 10.1007/s10107-012-0553-8 – volume: 12 start-page: 25 year: 2004 ident: 10.1016/j.na.2013.03.014_br000095 article-title: Prox-regular functions and sets in Banach spaces publication-title: Set-Valued Anal. doi: 10.1023/B:SVAN.0000023403.87092.a2 – year: 2009 ident: 10.1016/j.na.2013.03.014_br000085 – year: 2011 ident: 10.1016/j.na.2013.03.014_br000065 – ident: 10.1016/j.na.2013.03.014_br000025 – volume: 5 start-page: 43 year: 1980 ident: 10.1016/j.na.2013.03.014_br000120 article-title: Strongly regular generalized equations publication-title: Math. Oper. Res. doi: 10.1287/moor.5.1.43 – volume: 6 start-page: 1087 year: 1996 ident: 10.1016/j.na.2013.03.014_br000135 article-title: Characterizations of strong regularity for variational inequalities over polyhedral convex sets publication-title: SIAM J. Optim. doi: 10.1137/S1052623495284029 – volume: 15 start-page: 365 year: 2008 ident: 10.1016/j.na.2013.03.014_br000115 article-title: Charaterizations of metric regularity of subdifferentials publication-title: J. Convex Anal. – year: 2005 ident: 10.1016/j.na.2013.03.014_br000075 – volume: 348 start-page: 1805 year: 1996 ident: 10.1016/j.na.2013.03.014_br000090 article-title: Prox-regular functions in variational analysis publication-title: Trans. Amer. Math. Soc. doi: 10.1090/S0002-9947-96-01544-9 – ident: 10.1016/j.na.2013.03.014_br000105 – volume: 6 start-page: 363 year: 1998 ident: 10.1016/j.na.2013.03.014_br000145 article-title: Compactness properties, openness criteria and coderivatives publication-title: Set-Valued Anal. doi: 10.1023/A:1008746317549 – year: 1998 ident: 10.1016/j.na.2013.03.014_br000060 – volume: 10 start-page: 580 year: 2000 ident: 10.1016/j.na.2013.03.014_br000045 article-title: Stability of locally optimal solutions publication-title: SIAM J. Optim. doi: 10.1137/S1052623498348274 – ident: 10.1016/j.na.2013.03.014_br000035 doi: 10.1137/120887722 – volume: vol. 58 start-page: 32 year: 1992 ident: 10.1016/j.na.2013.03.014_br000050 article-title: Sensitivity analysis in nonsmooth optimization – volume: 74 start-page: 154 year: 2011 ident: 10.1016/j.na.2013.03.014_br000140 article-title: Second-order subdifferentials and convexity of real-valued functions publication-title: Nonlinear Anal. doi: 10.1016/j.na.2010.08.029 – year: 2008 ident: 10.1016/j.na.2013.03.014_br000125 – volume: 8 start-page: 287 year: 1998 ident: 10.1016/j.na.2013.03.014_br000005 article-title: Tilt stability of a local minimum publication-title: SIAM J. Optim. doi: 10.1137/S1052623496309296 – volume: 303 start-page: 1 year: 2005 ident: 10.1016/j.na.2013.03.014_br000100 article-title: Prox-regular functions in Hilbert spaces publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2004.06.003 – year: 2007 ident: 10.1016/j.na.2013.03.014_br000080 – volume: 22 start-page: 953 year: 2012 ident: 10.1016/j.na.2013.03.014_br000030 article-title: Second-order subdifferential calculus with applications to tilt stability in optimization publication-title: SIAM J. Optim. doi: 10.1137/110852528 – year: 2000 ident: 10.1016/j.na.2013.03.014_br000040 – volume: 75 start-page: 1260 year: 2012 ident: 10.1016/j.na.2013.03.014_br000015 article-title: A study of tilt-stable optimality and sufficient conditions publication-title: Nonlinear Anal. doi: 10.1016/j.na.2011.08.014 – ident: 10.1016/j.na.2013.03.014_br000130 – year: 2006 ident: 10.1016/j.na.2013.03.014_br000055 – volume: 23 start-page: 74 year: 2013 ident: 10.1016/j.na.2013.03.014_br000020 article-title: Partial smoothness, tilt stability, and generalized Hessians publication-title: SIAM J. Optim. doi: 10.1137/110852103 |
| SSID | ssj0001736 |
| Score | 2.246064 |
| Snippet | The paper is devoted to developing second-order tools of variational analysis and their applications to characterizing tilt-stable local minimizers of... |
| SourceID | proquest crossref elsevier |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 159 |
| SubjectTerms | Camber First-order and second-order generalized differentiation Lipschitzian stability Second-order growth Strong metric regularity Variational analysis and optimization |
| Title | Second-order variational analysis and characterizations of tilt-stable optimal solutions in infinite-dimensional spaces |
| URI | https://dx.doi.org/10.1016/j.na.2013.03.014 https://www.proquest.com/docview/1475522003 https://www.proquest.com/docview/1506384815 |
| Volume | 86 |
| WOSCitedRecordID | wos000318907300013&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: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1873-5215 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0001736 issn: 0362-546X databaseCode: AIEXJ dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1bb9MwFLZg44E9cBkgxk1GQkhoMsu1dh4L6gRoBCQyqW-WEzusY0tKk46JX89xbKcZg2o8oEZRGuVi9Xw9N_t8B6EXtGAMFL8kuSc8AgiJSBKogCgwLQCYXM9tdc0maJqy6TT5bOkJmq6dAK0qdn6ezP-rqOEcCFuXzv6DuPuHwgk4BqHDHsQO-ysJ_osOcSXpODV3zyAUduk-4fhHulK2nqj552oxXDs7aQm4i7qaqgZdcqqLSdxgdWYExjfTTiqRuimAIfTYBZ1U2JWI1stNDf-GWPTv7OUKw1p-O6pBP3X5nDer1Gv69cgs3M3gMx5mI3RnCOqyEasqrDjquhP2GpYNVaRvGcCNtfVNH6dLitzkFI5fV5obyg87IlpTbXqRMzv9xPcPDw54NplmL-ffiW4npqfdbW-V62gzoHECGntz_H4y_dAbaZ-GI8cspodrZ7DN0r-LL_2bx_Kb7e4ckuwOumUjCTw2CLiLrqlqG922UQW2OrvZRlsDykn49rHn6W3uoR9DsOABWLATHBxIfAksuC7xACzYggX3YMGzCv8JLNiA5T463J9kb98R24qDFOHIa0lBC8lGpfBFHEtVUhnTRICpYELFOYMtYqDJS3B2CwU6HeJaXUQWKaaoDFjhhQ_QRlVX6iHCUVkEYQ6BcuTnURjmiWS5TFQgQh8eI8UO2nM_Ny8sT71ul3LC3YLEY14JrgXEPdj8aAe96u-YG46WNdeGToLc-pjGd-SAvDV3PXfC5qB-9ZyaqFS9bCBypjGEMGAb11wT67hAsyI9usJzHqObqz_WE7TRLpbqKbpRnLWzZvHM4vgX0bG4Iw |
| linkProvider | Elsevier |
| 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=Second-order+variational+analysis+and+characterizations+of+tilt-stable+optimal+solutions+in+infinite-dimensional+spaces&rft.jtitle=Nonlinear+analysis&rft.au=Mordukhovich%2C+B+S&rft.au=Nghia%2C+T+T+A&rft.date=2013-07-01&rft.issn=0362-546X&rft.volume=86&rft.spage=159&rft.epage=180&rft_id=info:doi/10.1016%2Fj.na.2013.03.014&rft.externalDBID=NO_FULL_TEXT |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0362-546X&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0362-546X&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0362-546X&client=summon |