Inverse and implicit function theorems for H-differentiable and semismooth functions
In this article, we prove inverse and implicit function theorems for H-differentiable functions, thereby giving a unified treatment of such theorems for C 1 -functions, PC 1 -functions, and for locally Lipschitzian functions. We also derive inverse and implicit function theorems for semismooth funct...
Gespeichert in:
| Veröffentlicht in: | Optimization methods & software Jg. 19; H. 5; S. 443 - 461 |
|---|---|
| 1. Verfasser: | |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Taylor & Francis
01.10.2004
|
| Schlagworte: | |
| ISSN: | 1055-6788, 1029-4937 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | In this article, we prove inverse and implicit function theorems for H-differentiable functions, thereby giving a unified treatment of such theorems for C
1
-functions, PC
1
-functions, and for locally Lipschitzian functions. We also derive inverse and implicit function theorems for semismooth functions. |
|---|---|
| AbstractList | In this article, we prove inverse and implicit function theorems for H-differentiable functions, thereby giving a unified treatment of such theorems for C
1
-functions, PC
1
-functions, and for locally Lipschitzian functions. We also derive inverse and implicit function theorems for semismooth functions. |
| Author | Gowda, M. Seetharama |
| Author_xml | – sequence: 1 givenname: M. Seetharama surname: Gowda fullname: Gowda, M. Seetharama email: gowda@math.umbc.edu |
| BookMark | eNqFkN1KAzEQhYNUsK2-gRf7AqvJ5mcTb0SK2kLBm71fspuERnaTksSfvr0pLV5IsVczA-ebOXNmYOK80wDcIniHIIf3CFLKag4JghAiJmrG-AWYIliJkghcT_Y9pWXW8Cswi_E96wgibAqalfvUIepCOlXYcTvY3qbCfLg-We-KtNE-6DEWxodiWSprjA7aJSu74cBEPdo4ep82v1S8BpdGDlHfHOscNC_PzWJZrt9eV4unddljylIpO8FYVfVGEa4wV1x2hhtM8geVolQKLDjDEmJV50FS0SGIDYXG8EqYGs_Bw2FtH3yMQZs2e5d7BylIO7QItvt42lPxZJj8gbfBjjLszmHHm9blSEb55cOg2iR3gw8mSNfbeBJs03fK8ONZGP97_geT_ZEz |
| CitedBy_id | crossref_primary_10_1016_j_amc_2006_07_047 crossref_primary_10_1016_j_jde_2016_10_041 crossref_primary_10_1016_j_jmaa_2005_07_049 crossref_primary_10_1016_j_camwa_2011_10_046 crossref_primary_10_1016_j_camwa_2008_09_035 crossref_primary_10_1002_zamm_201500305 crossref_primary_10_1137_23M1565097 crossref_primary_10_1016_j_jmaa_2021_125895 crossref_primary_10_1007_s00158_009_0451_8 crossref_primary_10_1007_s10898_005_5880_3 crossref_primary_10_1007_s10957_015_0731_y crossref_primary_10_1016_j_jmaa_2016_11_045 crossref_primary_10_1007_s10589_007_9052_x crossref_primary_10_1155_2014_468065 crossref_primary_10_1007_s10957_010_9758_2 crossref_primary_10_15807_jorsj_54_12 crossref_primary_10_1002_zamm_200600039 crossref_primary_10_1007_BF02579053 crossref_primary_10_1007_s10107_025_02198_0 crossref_primary_10_1007_s10957_015_0842_5 crossref_primary_10_1007_s10957_008_9409_z crossref_primary_10_1007_s00158_007_0147_x crossref_primary_10_1007_s10107_007_0117_5 crossref_primary_10_1016_j_cma_2011_08_011 crossref_primary_10_1137_120887035 crossref_primary_10_1002_zamm_201200056 crossref_primary_10_1007_s10898_015_0312_5 crossref_primary_10_1016_j_nahs_2010_03_003 crossref_primary_10_1016_j_ejor_2007_11_032 crossref_primary_10_1287_moor_1070_0300 crossref_primary_10_1007_s10107_005_0629_9 crossref_primary_10_1137_070681235 crossref_primary_10_1287_moor_1060_0195 crossref_primary_10_1007_s00158_005_0591_4 crossref_primary_10_1287_moor_2024_0617 |
| Cites_doi | 10.1287/moor.16.2.292 10.1287/moor.22.2.301 10.1023/A:1026558500809 10.1023/A:1022996819381 10.1017/CBO9780511983658 10.2140/pjm.1976.64.97 10.1016/0024-3795(87)90339-9 10.1006/jmaa.1997.5358 10.1137/S0363012996311745 10.1007/BF00932859 10.1287/moor.5.1.101 10.1007/978-94-009-8177-5 10.1016/0024-3795(72)90019-5 10.1287/moor.5.4.510 10.1007/PL00011406 10.1287/moor.18.1.227 10.1016/S0167-6377(01)00073-6 10.1287/moor.25.3.400.12218 10.1007/978-1-4757-6388-1 10.1016/0167-6377(94)00059-F 10.1137/0315061 10.1137/S0895479894278940 10.1287/moor.27.1.150.342 10.1090/S0002-9939-1994-1215027-7 10.1007/BF00941302 10.1023/A:1026424918464 10.1287/moor.21.2.401 10.1137/S1052623496298194 10.1137/0508005 10.1287/moor.28.1.39.14258 10.1007/BF01580617 10.1007/BF01588782 10.1287/moor.17.3.691 10.1137/0803021 10.1006/jmaa.2000.7171 10.1007/BF02614394 10.1007/BF01581275 |
| ContentType | Journal Article |
| Copyright | Copyright Taylor & Francis Group, LLC 2004 |
| Copyright_xml | – notice: Copyright Taylor & Francis Group, LLC 2004 |
| DBID | AAYXX CITATION |
| DOI | 10.1080/10556780410001697668 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering |
| EISSN | 1029-4937 |
| EndPage | 461 |
| ExternalDocumentID | 10_1080_10556780410001697668 10051279 |
| GroupedDBID | .4S .7F .DC .QJ 0BK 0R~ 123 29N 30N 4.4 5VS AAENE AAGDL AAHIA AAJMT AALDU AAMIU AAPUL AAQRR ABCCY ABDBF ABFIM ABHAV ABJNI ABLIJ ABPAQ ABPEM ABTAI ABXUL ABXYU ACAGQ ACGEJ ACGFS ACIWK ACTIO ACUHS ADCVX ADGTB ADXPE AEISY AENEX AEOZL AEPSL AEYOC AFKVX AFRVT AGDLA AGMYJ AGROQ AHDZW AHMOU AIJEM AIYEW AJWEG AKBVH AKOOK ALCKM ALMA_UNASSIGNED_HOLDINGS ALQZU AMEWO AMVHM AQRUH AQTUD ARCSS AVBZW AWYRJ BLEHA CAG CCCUG CE4 COF CRFIH CS3 DGEBU DKSSO DMQIW DU5 EAP EBS EDO EMK EPL EST ESX E~A E~B F5P GTTXZ H13 HZ~ H~P I-F IPNFZ J.P KYCEM M4Z NA5 NY~ O9- P2P PQQKQ QCRFL RIG RNANH ROSJB RTWRZ S-T SNACF TASJS TBQAZ TDBHL TEJ TFL TFT TFW TOXWX TTHFI TUROJ TUS TWF UT5 UU3 ZGOLN ~S~ 07G 1TA AAIKQ AAKBW AAYXX ACGEE ACTCW AEUMN AGCQS AGLEN AMXXU BCCOT BPLKW C06 CITATION DWIFK EJD HF~ IVXBP LJTGL NUSFT TAQ TFMCV UB9 UU8 V3K V4Q |
| ID | FETCH-LOGICAL-c356t-ab96622cfd48d38d8abf8f341692d55a939863a03d75a9a59b103f50ff829f73 |
| IEDL.DBID | TFW |
| ISICitedReferencesCount | 41 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000224560700002&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1055-6788 |
| IngestDate | Sat Nov 29 02:36:02 EST 2025 Tue Nov 18 22:27:32 EST 2025 Mon Oct 20 23:45:42 EDT 2025 Mon May 13 12:09:11 EDT 2019 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 5 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c356t-ab96622cfd48d38d8abf8f341692d55a939863a03d75a9a59b103f50ff829f73 |
| PageCount | 19 |
| ParticipantIDs | crossref_primary_10_1080_10556780410001697668 informaworld_taylorfrancis_310_1080_10556780410001697668 crossref_citationtrail_10_1080_10556780410001697668 |
| PublicationCentury | 2000 |
| PublicationDate | 10/1/2004 2004-10-00 |
| PublicationDateYYYYMMDD | 2004-10-01 |
| PublicationDate_xml | – month: 10 year: 2004 text: 10/1/2004 day: 01 |
| PublicationDecade | 2000 |
| PublicationTitle | Optimization methods & software |
| PublicationYear | 2004 |
| Publisher | Taylor & Francis |
| Publisher_xml | – name: Taylor & Francis |
| References | b10 b54 b53 Warga J (b55) 1976 b56 b14 Pshenichny BN (b38) 1989 b16 b18 b19 Facchinei F (b11) 2003 Luo Z-Q (b27) 1996 b2 b8 b9 Ambrosetti A (b1) 1993 Cottle RW (b7) 1992 b21 b20 b23 b25 b24 Lloyd NG (b26) 1978 Chien MJ (b3) 1976; 3 b28 Qi L (b40) 1996 Fukushima M (b13) 1999 b30 b32 b31 b34 Clarke FH (b4) 1976; 64 b33 b36 b35 b37 b39 Mikhalevich VS (b29) 1987 Gowda MS (b15) 2000 Rockafellar RT (b46) 1970 Rudin W (b47) 1964 Clarke FH (b5) 1983 b41 b42 b45 b44 Klatte D (b22) 2002 Istratescu VI (b17) 1981 Samelson H (b48) 1958; 9 Clarke FH (b6) 1998 Ferris M (b12) 1997 Ralph D (b43) 1997; 76 b50 Scholtes S (b49) 1994 b52 b51 |
| References_xml | – ident: b44 doi: 10.1287/moor.16.2.292 – volume-title: Nonsmooth Analysis and Control Theory, Graduate Texts in Mathematics, Springer-Verlag year: 1998 ident: b6 – volume-title: Optimization and Nonsmooth Analysis, Wiley year: 1983 ident: b5 – ident: b41 doi: 10.1287/moor.22.2.301 – ident: b54 doi: 10.1023/A:1026558500809 – ident: b2 doi: 10.1023/A:1022996819381 – volume-title: Mathematical Programs with Equilibrium Constraints, Cambridge University Press year: 1996 ident: b27 doi: 10.1017/CBO9780511983658 – volume: 64 start-page: 97 year: 1976 ident: b4 publication-title: Pacific Journal of Mathematics doi: 10.2140/pjm.1976.64.97 – ident: b24 doi: 10.1016/0024-3795(87)90339-9 – volume-title: Introduction to Piecewise Differentiable Functions, Institute für Statistik und Mathematische Wirtschaftstheorie, Universität Karlsruhe year: 1994 ident: b49 – volume-title: Finite-Dimensional Variational Inequalities and Complementarity Problems, Springer-Verlag year: 2003 ident: b11 – ident: b32 doi: 10.1006/jmaa.1997.5358 – ident: b19 doi: 10.1137/S0363012996311745 – ident: b37 doi: 10.1007/BF00932859 – ident: b23 doi: 10.1287/moor.5.1.101 – volume-title: Fixed Point Theory, D. Reidel Publishing Co. year: 1981 ident: b17 doi: 10.1007/978-94-009-8177-5 – ident: b30 doi: 10.1016/0024-3795(72)90019-5 – volume-title: Department of Mathematics and Statistics, University of Maryland year: 2000 ident: b15 – ident: b50 doi: 10.1287/moor.5.4.510 – volume-title: Nonsmooth Equations in Optimization, Kluwer Academic Publishers year: 2002 ident: b22 – ident: b18 doi: 10.1007/PL00011406 – ident: b39 doi: 10.1287/moor.18.1.227 – ident: b52 doi: 10.1016/S0167-6377(01)00073-6 – ident: b51 doi: 10.1287/moor.25.3.400.12218 – volume-title: Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods year: 1999 ident: b13 doi: 10.1007/978-1-4757-6388-1 – ident: b9 doi: 10.1016/0167-6377(94)00059-F – volume-title: Methods of Nonconvex Optimization year: 1987 ident: b29 – ident: b28 doi: 10.1137/0315061 – ident: b14 doi: 10.1137/S0895479894278940 – volume-title: Complementarity and Variational Problems, State of the Art, SIAM Publications year: 1997 ident: b12 – volume-title: Convex Analysis, Princeton University Press year: 1970 ident: b46 – volume-title: Principles of Mathematical Analysis, McGraw-Hill year: 1964 ident: b47 – volume-title: Degree Theory, Cambridge University Press year: 1978 ident: b26 – ident: b53 doi: 10.1287/moor.27.1.150.342 – ident: b8 doi: 10.1090/S0002-9939-1994-1215027-7 – ident: b25 doi: 10.1007/BF00941302 – volume: 76 start-page: 593 year: 1997 ident: b43 publication-title: Mathematical Programming – ident: b21 doi: 10.1023/A:1026424918464 – volume: 9 start-page: 805 year: 1958 ident: b48 publication-title: Proceedings of the American Mathematical Society – volume-title: Calculus of Variations and Control Theory, Academic Press year: 1976 ident: b55 – ident: b35 doi: 10.1287/moor.21.2.401 – ident: b10 doi: 10.1137/S1052623496298194 – ident: b31 doi: 10.1137/0508005 – ident: b36 doi: 10.1287/moor.28.1.39.14258 – volume-title: Cambridge Studies in Advanced Mathematics, Cambridge University Press year: 1993 ident: b1 – volume-title: The Linear Complementarity Problem, Academic Press year: 1992 ident: b7 – volume: 3 start-page: 3 year: 1976 ident: b3 publication-title: Circuit Theory and Applications – ident: b33 doi: 10.1007/BF01580617 – ident: b20 doi: 10.1007/BF01588782 – ident: b45 doi: 10.1287/moor.17.3.691 – ident: b34 doi: 10.1137/0803021 – ident: b16 doi: 10.1006/jmaa.2000.7171 – ident: b56 doi: 10.1007/BF02614394 – start-page: pp. 371–391 volume-title: Ettore Majorana International Sci. Ser.: Phys. Sci. 43, Plenum Press year: 1989 ident: b38 – volume-title: School of Mathematics, The University of New South Wales year: 1996 ident: b40 – ident: b42 doi: 10.1007/BF01581275 |
| SSID | ssj0004146 |
| Score | 1.8919563 |
| Snippet | In this article, we prove inverse and implicit function theorems for H-differentiable functions, thereby giving a unified treatment of such theorems for C
1... |
| SourceID | crossref informaworld |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 443 |
| SubjectTerms | Coherent orientation Degree Generalized Jacobian H-differentiability Locally Lipschitzian functions Semismooth |
| Title | Inverse and implicit function theorems for H-differentiable and semismooth functions |
| URI | https://www.tandfonline.com/doi/abs/10.1080/10556780410001697668 |
| Volume | 19 |
| WOSCitedRecordID | wos000224560700002&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: PRVAWR databaseName: Taylor and Francis Online Journals customDbUrl: eissn: 1029-4937 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0004146 issn: 1055-6788 databaseCode: TFW dateStart: 19920101 isFulltext: true titleUrlDefault: https://www.tandfonline.com providerName: Taylor & Francis |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3LSsQwFL3I4EIXvsXxRRZug20zzWMp4jCrwUXB2ZU0TWBgHjKt4uebRzt2QEfQZaGnCb1JTtLeew7AnaaaWWKjOKaKYudojGXMClcr4_7DpDbs0ptNsPGYTybiuVPF79Iq3RnaBKEIv1a7yS2Lqs2Iu_eejl44x-9YLKFSV-1rmd_NzGz48lUY2ZQXWQC2CN7Wzv3wkA1u2lAu7XDO8PD_vT2Cg2a_iR7CADmGHb04gf2OCuEpZE5rY1VpZJtAU59hPq2RIzwXNBRKHecVsv1EI9w6qtiVoZgFTOU84-ZLG_M1qjqDbPiUPY5wY7aAFUlpjWVhDz5Jokw54CXhJZeF4cZyHBVJmaZSEMEpkREpmb2QqSjiiJg0MoYnwjByDr3FcqEvADElJFOaaaaigdaRsKNBS6JiYncnTJk-kPYt56oRInd-GLM8bvRKv3tlfcBr1GsQ4vjlftINYF77DyAmuJV8i8jrj7oPfAuKbGvw8u_QK9gL-pEuR_AaevXqTd_Arnqvp9Xq1g_pT_1v75s |
| linkProvider | Taylor & Francis |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1bS8MwGP3QKagP3sV57YOvwbZZc3kUcUycw4eCeytpmsBgF1mr-PNN0nZuMCeIj4WeJvRLc5L0-84BuFFEUUNsBAVEEmQdjZEIaGprZex_mMiEXTizCdrrsX6fv1TZhHmVVmn30LoUinBztf247WF0nRJ360wdnXKOW7IYRiVsHTYiQ7VWPj9uv36XRlYFRgaBDITV1XM_PGWBnRa0S-dYp733D_3dh91qyendlWPkANbU-BB25oQIjyC2chvTXHmmDW_gkswHhWc5z8bNK6sdR7lnOup1UG2qYiaHdFhicmsbN5qYsM9Q-THE7Yf4voMqvwUkcUQKJFKz9wlDqbMWyzDLmEg104bmCA-zKBIcc0aw8HFGzYWIeBr4WEe-1izkmuITaIwnY3UKHpVcUKmootJvKeVzMyCUwDLAZoFCpW4Crl9zIistcmuJMUyCSrJ02StrApqh3kotjl_ux_MRTAp3BqJLw5KliKT4LJrAVqDwqgbP_g69hq1O_NxNuo-9p3PYLuUkbcrgBTSK6bu6hE35UQzy6ZUb3188F_PF |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3PS8MwFH7oFNGDv8X5swevwbZZk_QoapkoY4eCu5U0TWAwt7FW8c83SdvZwZygx0K_JuS95r20730fwI0kkurARpBHBEFG0Rhxj6amV8b8hwm02bkVm6C9HhsMwn6ji9-UVZoztCqJIuxebV7uaabqirhbq-loiXNsxqIDKmHrsKEzZ2J8PI5evzsjq_4ijUAawurmuR-eshCcFqhLG0En2vv_dPdht0o4nbvSQw5gTY4PYadBQ3gEsSHbmOXS0UM4Q1tiPiwcE_GM1Zyy1_Etd_Q8nS6qJVX01pCOSkxuROPeJtroc1R-DHH0GN93UaW2gAQOSIF4qk8-vi9U1mEZZhnjqWJKBzkS-lkQ8BCHjGDu4ozqCx6EqediFbhKMT9UFJ9AazwZy1NwqAg5FZJKKtyOlG6o3UFyLDys0xMqVBtwvcqJqJjIjSDGKPEqwtJlS9YGNEdNSyaOX-7HTQMmhf0Cokq5kqWIpPgs2sBWoPCqAc_-Dr2Grf5DlLw89Z7PYbvkkjT1ghfQKmbv8hI2xUcxzGdX1ru_AFrQ8nc |
| 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=Inverse+and+implicit+function+theorems+for+H-differentiable+and+semismooth+functions&rft.jtitle=Optimization+methods+%26+software&rft.au=Gowda%2C+M.+Seetharama&rft.date=2004-10-01&rft.pub=Taylor+%26+Francis&rft.issn=1055-6788&rft.eissn=1029-4937&rft.volume=19&rft.issue=5&rft.spage=443&rft.epage=461&rft_id=info:doi/10.1080%2F10556780410001697668&rft.externalDocID=10051279 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1055-6788&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1055-6788&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1055-6788&client=summon |