A bundle-free implicit programming approach for a class of elliptic MPECs in function space

Using a standard first-order optimality condition for nonsmooth optimization problems, a general framework for a descent method is developed. This setting is applied to a class of mathematical programs with equilibrium constraints in function space from which a new algorithm is derived. Global conve...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Mathematical programming Jg. 160; H. 1-2; S. 271 - 305
Hauptverfasser:	Hintermüller, M., Surowiec, T.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2016 Springer Nature B.V
Schlagworte:	Algorithms Approximation Calculus of Variations and Optimal Control; Optimization Combinatorics Convergence Experiments Full Length Paper Function space Mathematical analysis Mathematical and Computational Physics Mathematical Methods in Physics Mathematical models Mathematical programming Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Optimization Partial differential equations Programming Studies Theoretical Implicit programming 49K21 49K20 Elliptic MPEC 49J52 90C33 Nonsmooth optimization 49M05 Optimal control of variational inequalities 65Kxx Elliptic variational inequality
ISSN:	0025-5610, 1436-4646
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Abstract	Using a standard first-order optimality condition for nonsmooth optimization problems, a general framework for a descent method is developed. This setting is applied to a class of mathematical programs with equilibrium constraints in function space from which a new algorithm is derived. Global convergence of the algorithm is demonstrated in function space and the results are then illustrated by numerical experiments.
AbstractList	Using a standard first-order optimality condition for nonsmooth optimization problems, a general framework for a descent method is developed. This setting is applied to a class of mathematical programs with equilibrium constraints in function space from which a new algorithm is derived. Global convergence of the algorithm is demonstrated in function space and the results are then illustrated by numerical experiments.
Author	Hintermüller, M. Surowiec, T.
Author_xml	– sequence: 1 givenname: M. surname: Hintermüller fullname: Hintermüller, M. organization: Department of Mathematics, Humboldt University of Berlin, Weierstrass Institute for Applied Analysis and Stochastics – sequence: 2 givenname: T. surname: Surowiec fullname: Surowiec, T. email: surowiec@math.hu-berlin.de organization: Department of Mathematics, Humboldt University of Berlin
BookMark	eNp9kE1LxDAQhoMouKv-AG8BL16ikzZpk6Ms6wcoetCTh5CmyRpp05q0B_-9WdaDCHoaBt5n5uVZov0wBIvQKYULClBfJgoUagK0IiBFSeQeWlBWVoRVrNpHC4CCE15ROETLlN4BgJZCLNDrFW7m0HaWuGgt9v3YeeMnPMZhE3Xf-7DBesybNm_YDRFrbDqdEh4ctl3nx8kb_PC0XiXsA3ZzMJMfAk6jNvYYHTjdJXvyPY_Qy_X6eXVL7h9v7lZX98SUTE6EWVk6biUDRnkjBWtrl0cjmsII5xhtTSOAcZDaGq1F63TN24ILXgOrZFEeofPd3VzzY7ZpUr1PJrfTwQ5zUlQwLkBUsszRs1_R92GOIbfLqaKGmsmS5hTdpUwcUorWqTH6XsdPRUFtdaudbpV1q61uJTNT_2KyRr2VMUXtu3_JYkem_CVsbPzR6U_oCzGqlP4
CODEN	MHPGA4
CitedBy_id	crossref_primary_10_1007_s11228_017_0408_9 crossref_primary_10_1016_j_jmaa_2021_125732 crossref_primary_10_1007_s00245_024_10162_1 crossref_primary_10_1080_01630563_2025_2488796 crossref_primary_10_1007_s11432_024_4397_7 crossref_primary_10_1137_18M1164925 crossref_primary_10_1137_22M1534420 crossref_primary_10_1007_s00245_023_10063_9 crossref_primary_10_1007_s10107_022_01893_6
Cites_doi	10.1007/BF00940933 10.2969/jmsj/02940615 10.1007/978-3-322-96752-7 10.1142/1493 10.1007/s10589-009-9307-9 10.1007/978-3-662-01569-8_3 10.1137/S1052623402407382 10.1051/cocv/2011105 10.1090/gsm/112 10.1007/978-3-322-96662-9 10.1017/CBO9780511983658 10.1137/100809325 10.1007/3-540-06583-0_26 10.1007/s11228-010-0158-4 10.1007/978-1-4612-1394-9 10.1007/BF02683341 10.1007/s002459911017 10.1002/mana.19921550110 10.1137/S1052623499361233 10.1051/m2an/2012049 10.2307/44152956 10.1137/S1052623401383558 10.4064/sm-57-2-147-190 10.1137/040611598 10.24033/bsmf.1663 10.1137/100802396 10.1287/moor.25.1.1.15213 10.1137/1.9780898718782 10.1007/978-3-642-45780-7_7 10.1137/080720681 10.1016/0022-1236(76)90017-3 10.1137/090764438 10.1137/S0363012996302615 10.1137/0322028
ContentType	Journal Article
Copyright	Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2016
Copyright_xml	– notice: Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2016
DBID	AAYXX CITATION 3V. 7SC 7WY 7WZ 7XB 87Z 88I 8AL 8AO 8FD 8FE 8FG 8FK 8FL ABJCF ABUWG AFKRA ARAPS AZQEC BENPR BEZIV BGLVJ CCPQU DWQXO FRNLG F~G GNUQQ HCIFZ JQ2 K60 K6~ K7- L.- L.0 L6V L7M L~C L~D M0C M0N M2P M7S P5Z P62 PHGZM PHGZT PKEHL PQBIZ PQBZA PQEST PQGLB PQQKQ PQUKI PRINS PTHSS Q9U
DOI	10.1007/s10107-016-0983-9
DatabaseName	CrossRef ProQuest Central (Corporate) Computer and Information Systems Abstracts ABI/INFORM Collection ABI/INFORM Global (PDF only) ProQuest Central (purchase pre-March 2016) ABI/INFORM Global (Alumni Edition) Science Database (Alumni Edition) Computing Database (Alumni Edition) ProQuest Pharma Collection Technology Research Database ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central (Alumni) (purchase pre-March 2016) ABI/INFORM Collection (Alumni Edition) Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection ProQuest Central Essentials ProQuest Central - New (Subscription) Business Premium Collection Technology collection ProQuest One Community College ProQuest Central Business Premium Collection (Alumni) ABI/INFORM Global (Corporate) ProQuest Central Student SciTech Premium Collection ProQuest Computer Science Collection ProQuest Business Collection (Alumni Edition) ProQuest Business Collection Computer Science Database ABI/INFORM Professional Advanced ABI/INFORM Professional Standard ProQuest Engineering Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional ABI/INFORM Global Computing Database Science Database Engineering Database Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Premium ProQuest One Academic ProQuest One Academic Middle East (New) ProQuest One Business (OCUL) ProQuest One Business (Alumni) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection ProQuest Central Basic
DatabaseTitle	CrossRef ProQuest Business Collection (Alumni Edition) Computer Science Database ProQuest Central Student ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection Computer and Information Systems Abstracts SciTech Premium Collection ProQuest Central China ABI/INFORM Complete ProQuest One Applied & Life Sciences ProQuest Central (New) Engineering Collection Advanced Technologies & Aerospace Collection Business Premium Collection ABI/INFORM Global Engineering Database ProQuest Science Journals (Alumni Edition) ProQuest One Academic Eastern Edition ProQuest Technology Collection ProQuest Business Collection ProQuest One Academic UKI Edition ProQuest One Academic ProQuest One Academic (New) ABI/INFORM Global (Corporate) ProQuest One Business Technology Collection Technology Research Database Computer and Information Systems Abstracts – Academic ProQuest One Academic Middle East (New) ProQuest Central (Alumni Edition) ProQuest One Community College ProQuest Pharma Collection ProQuest Central ABI/INFORM Professional Advanced ProQuest Engineering Collection ABI/INFORM Professional Standard ProQuest Central Korea Advanced Technologies Database with Aerospace ABI/INFORM Complete (Alumni Edition) ProQuest Computing ABI/INFORM Global (Alumni Edition) ProQuest Central Basic ProQuest Science Journals ProQuest Computing (Alumni Edition) ProQuest SciTech Collection Computer and Information Systems Abstracts Professional Advanced Technologies & Aerospace Database Materials Science & Engineering Collection ProQuest One Business (Alumni) ProQuest Central (Alumni) Business Premium Collection (Alumni)
DatabaseTitleList	Computer and Information Systems Abstracts ProQuest Business Collection (Alumni Edition)
Database_xml	– sequence: 1 dbid: BENPR name: ProQuest Central - New (Subscription) url: https://www.proquest.com/central sourceTypes: Aggregation Database
DeliveryMethod	fulltext_linktorsrc
Discipline	Engineering Mathematics
EISSN	1436-4646
EndPage	305
ExternalDocumentID	4208498161 10_1007_s10107_016_0983_9
Genre	Feature
GrantInformation_xml	– fundername: Deutsche Forschungsgemeinschaft grantid: HI 1466/5-1 funderid: http://dx.doi.org/10.13039/501100001659 – fundername: Einstein Stiftung Berlin grantid: C-OT1 funderid: http://dx.doi.org/10.13039/501100006188 – fundername: FWF grantid: SFB F32-N18 Subproject “Freelevel” – fundername: Einstein Stiftung Berlin grantid: Project C-OT1 funderid: http://dx.doi.org/10.13039/501100006188 – fundername: Deutsche Forschungsgemeinschaft grantid: HI 1466/2-1 funderid: http://dx.doi.org/10.13039/501100001659 – fundername: Deutsche Forschungsgemeinschaft grantid: SFB Transregio 154 Subproject B02 funderid: http://dx.doi.org/10.13039/501100001659
GroupedDBID	--K --Z -52 -5D -5G -BR -EM -Y2 -~C -~X .4S .86 .DC .VR 06D 0R~ 0VY 199 1B1 1N0 1OL 1SB 203 28- 29M 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2~H 30V 3V. 4.4 406 408 409 40D 40E 5GY 5QI 5VS 67Z 6NX 6TJ 78A 7WY 88I 8AO 8FE 8FG 8FL 8TC 8UJ 8VB 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 ABDBF ABDZT ABECU ABFTV ABHLI ABHQN ABJCF ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABUWG ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACGOD ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACNCT ACOKC ACOMO ACPIV ACUHS ACZOJ ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMOZ AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFEXP AFFNX AFGCZ AFKRA AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHQJS AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ AKVCP ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARAPS ARCSS ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN AZQEC B-. B0M BA0 BAPOH BBWZM BDATZ BENPR BEZIV BGLVJ BGNMA BPHCQ BSONS CAG CCPQU COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP DU5 DWQXO EAD EAP EBA EBLON EBR EBS EBU ECS EDO EIOEI EJD EMI EMK EPL ESBYG EST ESX FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRNLG FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNUQQ GNWQR GQ6 GQ7 GQ8 GROUPED_ABI_INFORM_COMPLETE GXS H13 HCIFZ HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ H~9 I-F I09 IAO IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ K1G K60 K6V K6~ K7- KDC KOV KOW L6V LAS LLZTM M0C M0N M2P M4Y M7S MA- N2Q N9A NB0 NDZJH NPVJJ NQ- NQJWS NU0 O9- O93 O9G O9I O9J OAM P19 P2P P62 P9R PF0 PQBIZ PQBZA PQQKQ PROAC PT4 PT5 PTHSS Q2X QOK QOS QWB R4E R89 R9I RHV RIG RNI RNS ROL RPX RPZ RSV RZK S16 S1Z S26 S27 S28 S3B SAP SCLPG SDD SDH SDM SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TH9 TN5 TSG TSK TSV TUC TUS U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WH7 WK8 XPP YLTOR Z45 Z5O Z7R Z7S Z7X Z7Y Z7Z Z81 Z83 Z86 Z88 Z8M Z8N Z8R Z8T Z8W Z92 ZL0 ZMTXR ZWQNP ~02 ~8M ~EX AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC ADHKG ADXHL AEZWR AFDZB AFFHD AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP AMVHM ATHPR AYFIA CITATION PHGZM PHGZT PQGLB 7SC 7XB 8AL 8FD 8FK JQ2 L.- L.0 L7M L~C L~D PKEHL PQEST PQUKI PRINS PUEGO Q9U
ID	FETCH-LOGICAL-c349t-4e93f5e940415b984d7fb98b8b2c8ff41dcb804509aecaa8dfa75d25857046923
IEDL.DBID	M2P
ISICitedReferencesCount	12
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000385191700010&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	0025-5610
IngestDate	Thu Oct 02 06:11:41 EDT 2025 Thu Sep 25 00:38:47 EDT 2025 Sat Nov 29 03:33:59 EST 2025 Tue Nov 18 20:40:21 EST 2025 Fri Feb 21 02:32:35 EST 2025
IsPeerReviewed	true
IsScholarly	true
Issue	1-2
Keywords	Implicit programming 49K21 49K20 Elliptic MPEC 49J52 90C33 Nonsmooth optimization 49M05 Optimal control of variational inequalities 65Kxx Elliptic variational inequality
Language	English
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c349t-4e93f5e940415b984d7fb98b8b2c8ff41dcb804509aecaa8dfa75d25857046923
Notes	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-1 ObjectType-Feature-2 content type line 23
PQID	1827074931
PQPubID	25307
PageCount	35
ParticipantIDs	proquest_miscellaneous_1845808693 proquest_journals_1827074931 crossref_primary_10_1007_s10107_016_0983_9 crossref_citationtrail_10_1007_s10107_016_0983_9 springer_journals_10_1007_s10107_016_0983_9
PublicationCentury	2000
PublicationDate	20161100 2016-11-00 20161101
PublicationDateYYYYMMDD	2016-11-01
PublicationDate_xml	– month: 11 year: 2016 text: 20161100
PublicationDecade	2010
PublicationPlace	Berlin/Heidelberg
PublicationPlace_xml	– name: Berlin/Heidelberg – name: Heidelberg
PublicationSubtitle	A Publication of the Mathematical Optimization Society
PublicationTitle	Mathematical programming
PublicationTitleAbbrev	Math. Program
PublicationYear	2016
Publisher	Springer Berlin Heidelberg Springer Nature B.V
Publisher_xml	– name: Springer Berlin Heidelberg – name: Springer Nature B.V
References	HintermüllerMItoKKunischKThe primal–dual active set strategy as a semismooth Newton methodSIAM J. Optim.20021386588819722191080.9007410.1137/S1052623401383558 HenrotAPierreMVariation et optimisation de formes, vol. 48 of Mathématiques & Applications (Berlin) [Mathematics & Applications]2005BerlinSpringer BergouniouxMOptimal control of an obstacle problemAppl. Math. Optim.1997362147172145543210.1007/BF02683341 HintermüllerMKunischKPath-following methods for a class of constrained minimization problems in function spaceSIAM J. Optim.200617115918722191491137.4902810.1137/040611598(electronic) HintermüllerMMordukhovichBSurowiecTSeveral approaches for the derivation of stationarity conditions for elliptic MPECs with upper-level control constraintsMath. Program.2013146155558232326261332.90300 Lions, J.-L.: Various topics in the theory of optimal control of distributed systems. In: Optimal control theory and its applications (Proc. Fourteenth Biennial Sem. Canad. Math. Congr., Univ. Western Ontario, London, Ont., 1973), Part I. Springer, Berlin, 1974, pp. 116–309. Lecture Notes in Econom. and Math. Systems, Vol. 105 BergouniouxMOptimal control of problems governed by abstract elliptic variational inequalities with state constraintsSIAM J. Control Optim.199836127328916165900919.4900210.1137/S0363012996302615(electronic) ChoquetGTheory of capacitiesAnn. Inst. Fourier Grenoble195551953–1954131295807600064.35101 Preiss, D., Zajíček, L.: Sigma-porous sets in products of metric spaces and sigma-directionally porous sets in Banach spaces. Real Anal. Exchange 24(1), 295–313 (1998/99) BrezisHRStampacchiaGSur la régularité de la solution d’inéquations elliptiquesBull. Soc. Math. Fr.1968961531802393020165.45601 ScheelHScholtesSMathematical programs with complementarity constraints: stationarity, optimality, and sensitivityMath. Oper. Res.200025112218543171073.9055710.1287/moor.25.1.1.15213 LionsJ-LContrôle des systèmes distribués singuliers, vol. 13 of Méthodes Mathématiques de l’Informatique [Mathematical Methods of Information Science]1983MontrougeGauthier-Villars BonnansJ-FShapiroAPerturbation Analysis of Optimization Problems2000BerlinSpringer0966.4900110.1007/978-1-4612-1394-9 OutrataJKočvaraMZoweJNonsmooth Approach to Optimization Problems with Equilibrium Constraints, Vol. 28 of Nonconvex Optimization and Its Applications1998DordrechtKluwer Academic Publishers0947.90093 HarauxAHow to differentiate the projection on a convex set in Hilbert space. Some applications to variational inequalitiesJ. Math. Soc. Jpn.19772946156314810600387.4602210.2969/jmsj/02940615 MignotFPuelJ-POptimal control in some variational inequalitiesSIAM J. Control Optim.19842234664767398360561.4900710.1137/0322028 Yvon, J.P.: Optimal control of systems governed by variational inequalities. In: Fifth Conference on Optimization Techniques (Rome, 1973), Part I. Lecture Notes in Comput. Sci., Vol. 3. Springer, Berlin, pp. 265–275 (1973) ShapiroAOn concepts of directional differentiabilityJOTA199066347748710802590682.4901510.1007/BF00940933 Yvon, J.-P.: Etude de quelques problèmes de contrôle pour des systèmes distribués. PhD thesis, 1973 Paris VI FletcherRLeyfferSRalphDScholtesSLocal convergence of SQP methods for mathematical programs with equilibrium constraintsSIAM J. Optim.200617125928622191531112.9009810.1137/S1052623402407382(electronic) Schiela, A., Wachsmuth, D.: Convergence analysis of smoothing methods for optimal control of stationary variational inequalities. DFG Research Center MATHEON Preprint. http://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1035, January 2012 AdamsRAFournierJJ-FSobolev Spaces20082AmsterdamElsevier0385.46024 Fukushima, M., Pang, J.-S.: Convergence of a smoothing continuation method for mathematical programs with complementarity constraints. In: Ill-posed variational problems and regularization techniques (Trier, 1998). vol. 477 of Lecture Notes in Econom. and Math. Systems. Springer, Berlin, pp. 99–110 OutrataJVJařusekJStaráJOn optimality conditions in control of elliptic variational inequalitiesSet-Valued Var. Anal.201119234227708951211.4903610.1007/s11228-010-0158-4 BarbuVOptimal Control of Variational Inequalities, Volume 100 of Research Notes in Mathematics1984Boston, MAPitman (Advanced Publishing Program) ScholtesSConvergence properties of a regularization scheme for mathematical programs with complementarity constraintsSIAM J. Optim.200111491893618552141010.9008610.1137/S1052623499361233(electronic) HintermüllerMSurowiecTFirst order optimality conditions for elliptic mathematical programs with equilibrium constraints via variational analysisSIAM J. Optim.20122141561159328695081248.4903010.1137/100802396 MäkeläMMNeittaanmäkiPNonsmooth Optimization: Analysis and Algorithms with Applications to Optimal Control1992River EdgeWorld Scientific Publishing Co. Inc.0757.4901710.1142/1493 KunischKWachsmuthDSufficient optimality conditions and semi-smooth Newton methods for optimal control of stationary variational inequalitiesESAIM Control Optim. Calc. Var.201218452054729546371246.4902110.1051/cocv/2011105 De Los ReyesJCOptimal control of a class of variational inequalities of the second kindSIAM J. Control Optim.20114941629165828375691226.4900810.1137/090764438 HackbuschWMultigrid Methods and Applications, Volume 4 of Springer Series in Computational Mathematics1985BerlinSpringer AttouchHButtazzoGMichailleGVariational Analysis in Sobolev and BV Spaces. MPS-SIAM Series on Optimization2006PhiladelphiaSIAM and MPS1095.4900110.1137/1.9780898718782 MignotFContrôle dans les inéquations variationelles elliptiquesJ. Funct. Anal.19762221301854231550364.4900310.1016/0022-1236(76)90017-3 ItoKKunischKOptimal control of elliptic variational inequalitiesAppl. Math. Optim.200041334336417394000960.4900310.1007/s002459911017 Glowinski, R., Lions, J.-L., Trémolières, R.: Analyse numérique des inéquations variationnelles. Tome 1. Dunod, Paris, 1976. Théorie générale premiéres applications, Méthodes Mathématiques de l’Informatique, 5 LuoZ-QPangJ-SRalphDMathematical Programs with Equilibrium Constraints1996CambridgeCambridge University Press1139.9000310.1017/CBO9780511983658 Großmann, C., Roos, H.-G.: Numerik partieller Differentialgleichungen. second ed. Teubner Studienbücher Mathematik. [Teubner Mathematical Textbooks]. B. G. Teubner, Stuttgart, (1994) RodriguesJ-FObstacle Problems in Mathematical Physics. No. 134 in North-Holland Mathematics Studies1984AmsterdamNorth-Holland Publishing Co. HerzogRMeyerCWachsmuthGC-stationarity for optimal control of static plasticity with linear kinematic hardeningSIAM J. Control Optim.20125053052308230220981321.4901510.1137/100809325 Červinka, M.: Hierarchical Structures in Equilibrium Problems. PhD thesis, Charles University in Prague (2008) HintermüllerMKopackaIMathematical programs with complementarity constraints in function space: C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C$$\end{document}- and strong stationarity and a path-following algorithmSIAM J. Optim.200920286890225158011189.4903210.1137/080720681 ClarkeFHOptimization and Nonsmooth Analysis, Canadian Mathematical Society Series of Monographs and Advanced Texts1983New YorkWiley Tröltzsch, F.: Optimal control of partial differential equations, vol. 112 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2010. Theory, methods and applications, Translated from the 2005 German original by Jürgen Sprekels GoldbergHKampowskyWTröltzschFOn Nemytskij operators in Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_p$$\end{document}-spaces of abstract functionsMath. Nachr.199215512714012312600760.4703110.1002/mana.19921550110 KinderlehrerDStampacchiaGAn Introduction to Variational Inequalities and Their Applications1980New YorkAcademic Press0457.35001 AronszajnNDifferentiability of Lipschitzian mappings between Banach spacesStudia Math.19765721471904256080342.46034 HintermüllerMKopackaIA smooth penalty approach and a nonlinear multigrid algorithm for elliptic MPECsComput. Optim. Appl.201150111114528228181229.4903210.1007/s10589-009-9307-9 SchielaAWachsmuthDConvergence analysis of smoothing methods for optimal control of stationary variational inequalities with control constraintsESAIM Math. Model. Numer. Anal.201347377178730564081266.6511210.1051/m2an/2012049 WlokaJPartielle Differentialgleichungen1982LeipzigBSB B.G. Teubner Verlagsgesellschaft0482.3500110.1007/978-3-322-96662-9 K Kunisch (983_CR29) 2012; 18 A Shapiro (983_CR44) 1990; 66 S Scholtes (983_CR43) 2001; 11 RA Adams (983_CR1) 2008 J-L Lions (983_CR31) 1983 HR Brezis (983_CR8) 1968; 96 Z-Q Luo (983_CR32) 1996 983_CR30 J-F Rodrigues (983_CR39) 1984 H Attouch (983_CR3) 2006 M Hintermüller (983_CR25) 2013; 146 983_CR38 JC Los Reyes De (983_CR11) 2011; 49 M Bergounioux (983_CR6) 1998; 36 J-F Bonnans (983_CR7) 2000 M Hintermüller (983_CR23) 2011; 50 F Mignot (983_CR34) 1976; 22 D Kinderlehrer (983_CR28) 1980 FH Clarke (983_CR10) 1983 J Wloka (983_CR47) 1982 MM Mäkelä (983_CR33) 1992 M Hintermüller (983_CR21) 2002; 13 A Haraux (983_CR18) 1977; 29 F Mignot (983_CR35) 1984; 22 H Scheel (983_CR40) 2000; 25 N Aronszajn (983_CR2) 1976; 57 M Bergounioux (983_CR5) 1997; 36 H Goldberg (983_CR15) 1992; 155 JV Outrata (983_CR37) 2011; 19 V Barbu (983_CR4) 1984 G Choquet (983_CR9) 1955; 5 983_CR14 983_CR13 983_CR16 R Herzog (983_CR20) 2012; 50 M Hintermüller (983_CR24) 2006; 17 A Schiela (983_CR42) 2013; 47 M Hintermüller (983_CR22) 2009; 20 M Hintermüller (983_CR26) 2012; 21 K Ito (983_CR27) 2000; 41 W Hackbusch (983_CR17) 1985 983_CR41 J Outrata (983_CR36) 1998 R Fletcher (983_CR12) 2006; 17 983_CR45 A Henrot (983_CR19) 2005 983_CR46 983_CR49 983_CR48
References_xml	– reference: AdamsRAFournierJJ-FSobolev Spaces20082AmsterdamElsevier0385.46024 – reference: WlokaJPartielle Differentialgleichungen1982LeipzigBSB B.G. Teubner Verlagsgesellschaft0482.3500110.1007/978-3-322-96662-9 – reference: BergouniouxMOptimal control of problems governed by abstract elliptic variational inequalities with state constraintsSIAM J. Control Optim.199836127328916165900919.4900210.1137/S0363012996302615(electronic) – reference: HintermüllerMKopackaIMathematical programs with complementarity constraints in function space: C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C$$\end{document}- and strong stationarity and a path-following algorithmSIAM J. Optim.200920286890225158011189.4903210.1137/080720681 – reference: BonnansJ-FShapiroAPerturbation Analysis of Optimization Problems2000BerlinSpringer0966.4900110.1007/978-1-4612-1394-9 – reference: FletcherRLeyfferSRalphDScholtesSLocal convergence of SQP methods for mathematical programs with equilibrium constraintsSIAM J. Optim.200617125928622191531112.9009810.1137/S1052623402407382(electronic) – reference: MignotFContrôle dans les inéquations variationelles elliptiquesJ. Funct. Anal.19762221301854231550364.4900310.1016/0022-1236(76)90017-3 – reference: HackbuschWMultigrid Methods and Applications, Volume 4 of Springer Series in Computational Mathematics1985BerlinSpringer – reference: RodriguesJ-FObstacle Problems in Mathematical Physics. No. 134 in North-Holland Mathematics Studies1984AmsterdamNorth-Holland Publishing Co. – reference: SchielaAWachsmuthDConvergence analysis of smoothing methods for optimal control of stationary variational inequalities with control constraintsESAIM Math. Model. Numer. Anal.201347377178730564081266.6511210.1051/m2an/2012049 – reference: ClarkeFHOptimization and Nonsmooth Analysis, Canadian Mathematical Society Series of Monographs and Advanced Texts1983New YorkWiley – reference: Tröltzsch, F.: Optimal control of partial differential equations, vol. 112 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2010. Theory, methods and applications, Translated from the 2005 German original by Jürgen Sprekels – reference: Yvon, J.-P.: Etude de quelques problèmes de contrôle pour des systèmes distribués. PhD thesis, 1973 Paris VI – reference: BarbuVOptimal Control of Variational Inequalities, Volume 100 of Research Notes in Mathematics1984Boston, MAPitman (Advanced Publishing Program) – reference: MäkeläMMNeittaanmäkiPNonsmooth Optimization: Analysis and Algorithms with Applications to Optimal Control1992River EdgeWorld Scientific Publishing Co. Inc.0757.4901710.1142/1493 – reference: Großmann, C., Roos, H.-G.: Numerik partieller Differentialgleichungen. second ed. Teubner Studienbücher Mathematik. [Teubner Mathematical Textbooks]. B. G. Teubner, Stuttgart, (1994) – reference: Glowinski, R., Lions, J.-L., Trémolières, R.: Analyse numérique des inéquations variationnelles. Tome 1. Dunod, Paris, 1976. Théorie générale premiéres applications, Méthodes Mathématiques de l’Informatique, 5 – reference: Lions, J.-L.: Various topics in the theory of optimal control of distributed systems. In: Optimal control theory and its applications (Proc. Fourteenth Biennial Sem. Canad. Math. Congr., Univ. Western Ontario, London, Ont., 1973), Part I. Springer, Berlin, 1974, pp. 116–309. Lecture Notes in Econom. and Math. Systems, Vol. 105 – reference: AronszajnNDifferentiability of Lipschitzian mappings between Banach spacesStudia Math.19765721471904256080342.46034 – reference: HintermüllerMKunischKPath-following methods for a class of constrained minimization problems in function spaceSIAM J. Optim.200617115918722191491137.4902810.1137/040611598(electronic) – reference: ItoKKunischKOptimal control of elliptic variational inequalitiesAppl. Math. Optim.200041334336417394000960.4900310.1007/s002459911017 – reference: Fukushima, M., Pang, J.-S.: Convergence of a smoothing continuation method for mathematical programs with complementarity constraints. In: Ill-posed variational problems and regularization techniques (Trier, 1998). vol. 477 of Lecture Notes in Econom. and Math. Systems. Springer, Berlin, pp. 99–110 – reference: ScheelHScholtesSMathematical programs with complementarity constraints: stationarity, optimality, and sensitivityMath. Oper. Res.200025112218543171073.9055710.1287/moor.25.1.1.15213 – reference: ShapiroAOn concepts of directional differentiabilityJOTA199066347748710802590682.4901510.1007/BF00940933 – reference: OutrataJKočvaraMZoweJNonsmooth Approach to Optimization Problems with Equilibrium Constraints, Vol. 28 of Nonconvex Optimization and Its Applications1998DordrechtKluwer Academic Publishers0947.90093 – reference: Červinka, M.: Hierarchical Structures in Equilibrium Problems. PhD thesis, Charles University in Prague (2008) – reference: HerzogRMeyerCWachsmuthGC-stationarity for optimal control of static plasticity with linear kinematic hardeningSIAM J. Control Optim.20125053052308230220981321.4901510.1137/100809325 – reference: BergouniouxMOptimal control of an obstacle problemAppl. Math. Optim.1997362147172145543210.1007/BF02683341 – reference: HintermüllerMSurowiecTFirst order optimality conditions for elliptic mathematical programs with equilibrium constraints via variational analysisSIAM J. Optim.20122141561159328695081248.4903010.1137/100802396 – reference: ChoquetGTheory of capacitiesAnn. Inst. Fourier Grenoble195551953–1954131295807600064.35101 – reference: BrezisHRStampacchiaGSur la régularité de la solution d’inéquations elliptiquesBull. Soc. Math. Fr.1968961531802393020165.45601 – reference: GoldbergHKampowskyWTröltzschFOn Nemytskij operators in Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_p$$\end{document}-spaces of abstract functionsMath. Nachr.199215512714012312600760.4703110.1002/mana.19921550110 – reference: Yvon, J.P.: Optimal control of systems governed by variational inequalities. In: Fifth Conference on Optimization Techniques (Rome, 1973), Part I. Lecture Notes in Comput. Sci., Vol. 3. Springer, Berlin, pp. 265–275 (1973) – reference: Preiss, D., Zajíček, L.: Sigma-porous sets in products of metric spaces and sigma-directionally porous sets in Banach spaces. Real Anal. Exchange 24(1), 295–313 (1998/99) – reference: MignotFPuelJ-POptimal control in some variational inequalitiesSIAM J. Control Optim.19842234664767398360561.4900710.1137/0322028 – reference: HintermüllerMKopackaIA smooth penalty approach and a nonlinear multigrid algorithm for elliptic MPECsComput. Optim. Appl.201150111114528228181229.4903210.1007/s10589-009-9307-9 – reference: LuoZ-QPangJ-SRalphDMathematical Programs with Equilibrium Constraints1996CambridgeCambridge University Press1139.9000310.1017/CBO9780511983658 – reference: AttouchHButtazzoGMichailleGVariational Analysis in Sobolev and BV Spaces. MPS-SIAM Series on Optimization2006PhiladelphiaSIAM and MPS1095.4900110.1137/1.9780898718782 – reference: LionsJ-LContrôle des systèmes distribués singuliers, vol. 13 of Méthodes Mathématiques de l’Informatique [Mathematical Methods of Information Science]1983MontrougeGauthier-Villars – reference: OutrataJVJařusekJStaráJOn optimality conditions in control of elliptic variational inequalitiesSet-Valued Var. Anal.201119234227708951211.4903610.1007/s11228-010-0158-4 – reference: HintermüllerMMordukhovichBSurowiecTSeveral approaches for the derivation of stationarity conditions for elliptic MPECs with upper-level control constraintsMath. Program.2013146155558232326261332.90300 – reference: ScholtesSConvergence properties of a regularization scheme for mathematical programs with complementarity constraintsSIAM J. Optim.200111491893618552141010.9008610.1137/S1052623499361233(electronic) – reference: HintermüllerMItoKKunischKThe primal–dual active set strategy as a semismooth Newton methodSIAM J. Optim.20021386588819722191080.9007410.1137/S1052623401383558 – reference: KinderlehrerDStampacchiaGAn Introduction to Variational Inequalities and Their Applications1980New YorkAcademic Press0457.35001 – reference: HenrotAPierreMVariation et optimisation de formes, vol. 48 of Mathématiques & Applications (Berlin) [Mathematics & Applications]2005BerlinSpringer – reference: HarauxAHow to differentiate the projection on a convex set in Hilbert space. Some applications to variational inequalitiesJ. Math. Soc. Jpn.19772946156314810600387.4602210.2969/jmsj/02940615 – reference: De Los ReyesJCOptimal control of a class of variational inequalities of the second kindSIAM J. Control Optim.20114941629165828375691226.4900810.1137/090764438 – reference: KunischKWachsmuthDSufficient optimality conditions and semi-smooth Newton methods for optimal control of stationary variational inequalitiesESAIM Control Optim. Calc. Var.201218452054729546371246.4902110.1051/cocv/2011105 – reference: Schiela, A., Wachsmuth, D.: Convergence analysis of smoothing methods for optimal control of stationary variational inequalities. DFG Research Center MATHEON Preprint. http://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1035, January 2012 – volume: 146 start-page: 555 issue: 1 year: 2013 ident: 983_CR25 publication-title: Math. Program. – volume-title: Nonsmooth Approach to Optimization Problems with Equilibrium Constraints, Vol. 28 of Nonconvex Optimization and Its Applications year: 1998 ident: 983_CR36 – volume: 66 start-page: 477 issue: 3 year: 1990 ident: 983_CR44 publication-title: JOTA doi: 10.1007/BF00940933 – volume: 29 start-page: 615 issue: 4 year: 1977 ident: 983_CR18 publication-title: J. Math. Soc. Jpn. doi: 10.2969/jmsj/02940615 – ident: 983_CR16 doi: 10.1007/978-3-322-96752-7 – volume-title: An Introduction to Variational Inequalities and Their Applications year: 1980 ident: 983_CR28 – ident: 983_CR46 – volume-title: Optimal Control of Variational Inequalities, Volume 100 of Research Notes in Mathematics year: 1984 ident: 983_CR4 – volume-title: Nonsmooth Optimization: Analysis and Algorithms with Applications to Optimal Control year: 1992 ident: 983_CR33 doi: 10.1142/1493 – ident: 983_CR14 – volume-title: Sobolev Spaces year: 2008 ident: 983_CR1 – volume: 50 start-page: 111 issue: 1 year: 2011 ident: 983_CR23 publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-009-9307-9 – ident: 983_CR41 – ident: 983_CR30 doi: 10.1007/978-3-662-01569-8_3 – volume: 17 start-page: 259 issue: 1 year: 2006 ident: 983_CR12 publication-title: SIAM J. Optim. doi: 10.1137/S1052623402407382 – volume: 18 start-page: 520 issue: 4 year: 2012 ident: 983_CR29 publication-title: ESAIM Control Optim. Calc. Var. doi: 10.1051/cocv/2011105 – volume-title: Contrôle des systèmes distribués singuliers, vol. 13 of Méthodes Mathématiques de l’Informatique [Mathematical Methods of Information Science] year: 1983 ident: 983_CR31 – volume-title: Optimization and Nonsmooth Analysis, Canadian Mathematical Society Series of Monographs and Advanced Texts year: 1983 ident: 983_CR10 – ident: 983_CR45 doi: 10.1090/gsm/112 – volume-title: Partielle Differentialgleichungen year: 1982 ident: 983_CR47 doi: 10.1007/978-3-322-96662-9 – volume-title: Mathematical Programs with Equilibrium Constraints year: 1996 ident: 983_CR32 doi: 10.1017/CBO9780511983658 – volume-title: Multigrid Methods and Applications, Volume 4 of Springer Series in Computational Mathematics year: 1985 ident: 983_CR17 – volume: 50 start-page: 3052 issue: 5 year: 2012 ident: 983_CR20 publication-title: SIAM J. Control Optim. doi: 10.1137/100809325 – ident: 983_CR49 doi: 10.1007/3-540-06583-0_26 – volume: 19 start-page: 23 year: 2011 ident: 983_CR37 publication-title: Set-Valued Var. Anal. doi: 10.1007/s11228-010-0158-4 – volume-title: Perturbation Analysis of Optimization Problems year: 2000 ident: 983_CR7 doi: 10.1007/978-1-4612-1394-9 – volume: 36 start-page: 147 issue: 2 year: 1997 ident: 983_CR5 publication-title: Appl. Math. Optim. doi: 10.1007/BF02683341 – ident: 983_CR48 – volume: 41 start-page: 343 issue: 3 year: 2000 ident: 983_CR27 publication-title: Appl. Math. Optim. doi: 10.1007/s002459911017 – volume: 155 start-page: 127 year: 1992 ident: 983_CR15 publication-title: Math. Nachr. doi: 10.1002/mana.19921550110 – volume: 11 start-page: 918 issue: 4 year: 2001 ident: 983_CR43 publication-title: SIAM J. Optim. doi: 10.1137/S1052623499361233 – volume-title: Variation et optimisation de formes, vol. 48 of Mathématiques & Applications (Berlin) [Mathematics & Applications] year: 2005 ident: 983_CR19 – volume: 47 start-page: 771 issue: 3 year: 2013 ident: 983_CR42 publication-title: ESAIM Math. Model. Numer. Anal. doi: 10.1051/m2an/2012049 – ident: 983_CR38 doi: 10.2307/44152956 – volume: 13 start-page: 865 year: 2002 ident: 983_CR21 publication-title: SIAM J. Optim. doi: 10.1137/S1052623401383558 – volume: 57 start-page: 147 issue: 2 year: 1976 ident: 983_CR2 publication-title: Studia Math. doi: 10.4064/sm-57-2-147-190 – volume: 17 start-page: 159 issue: 1 year: 2006 ident: 983_CR24 publication-title: SIAM J. Optim. doi: 10.1137/040611598 – volume: 96 start-page: 153 year: 1968 ident: 983_CR8 publication-title: Bull. Soc. Math. Fr. doi: 10.24033/bsmf.1663 – volume: 21 start-page: 1561 issue: 4 year: 2012 ident: 983_CR26 publication-title: SIAM J. Optim. doi: 10.1137/100802396 – volume: 25 start-page: 1 issue: 1 year: 2000 ident: 983_CR40 publication-title: Math. Oper. Res. doi: 10.1287/moor.25.1.1.15213 – volume-title: Variational Analysis in Sobolev and BV Spaces. MPS-SIAM Series on Optimization year: 2006 ident: 983_CR3 doi: 10.1137/1.9780898718782 – ident: 983_CR13 doi: 10.1007/978-3-642-45780-7_7 – volume-title: Obstacle Problems in Mathematical Physics. No. 134 in North-Holland Mathematics Studies year: 1984 ident: 983_CR39 – volume: 5 start-page: 131 issue: 1953–1954 year: 1955 ident: 983_CR9 publication-title: Ann. Inst. Fourier Grenoble – volume: 20 start-page: 868 issue: 2 year: 2009 ident: 983_CR22 publication-title: SIAM J. Optim. doi: 10.1137/080720681 – volume: 22 start-page: 130 issue: 2 year: 1976 ident: 983_CR34 publication-title: J. Funct. Anal. doi: 10.1016/0022-1236(76)90017-3 – volume: 49 start-page: 1629 issue: 4 year: 2011 ident: 983_CR11 publication-title: SIAM J. Control Optim. doi: 10.1137/090764438 – volume: 36 start-page: 273 issue: 1 year: 1998 ident: 983_CR6 publication-title: SIAM J. Control Optim. doi: 10.1137/S0363012996302615 – volume: 22 start-page: 466 issue: 3 year: 1984 ident: 983_CR35 publication-title: SIAM J. Control Optim. doi: 10.1137/0322028
SSID	ssj0001388
Score	2.2295737
Snippet	Using a standard first-order optimality condition for nonsmooth optimization problems, a general framework for a descent method is developed. This setting is...
SourceID	proquest crossref springer
SourceType	Aggregation Database Enrichment Source Index Database Publisher
StartPage	271
SubjectTerms	Algorithms Approximation Calculus of Variations and Optimal Control; Optimization Combinatorics Convergence Experiments Full Length Paper Function space Mathematical analysis Mathematical and Computational Physics Mathematical Methods in Physics Mathematical models Mathematical programming Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Optimization Partial differential equations Programming Studies Theoretical
SummonAdditionalLinks	– databaseName: SpringerLINK Contemporary 1997-Present dbid: RSV link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LS8QwEB58HfTgW1xfRPCkBOyLJMdFXDyoLL5Y8FCSNIEF7cq26-93ptvurqKCnkppkoY8Zr5hZr4BODHKhzazmktrLSfHGTeJEDzOMoHaSJuw8p4_XYvbW9nrqW6dx1000e6NS7KS1DPJbkEVJokWsJIRV_OwiNpOUr2Gu_unifgNIimbOq0EDhpX5ndDfFZGU4T5xSla6ZrO2r9muQ6rNbRk7fFZ2IA5l2_CygzhIL7dTFhaiy14bjMzIpIF7ofOsX4VXN4vWR2z9YpdWMM5zhDcMs0sgW028Ix4PFHaWHbTvbwoWD9npCFplxnKKOu24bFz-XBxxetiC9xGsSp57FTkE6diytk3SsaZ8Pgw0oRWeh8HmTUS8d-50s5qLTOvRZKFCRHko4kdRjuwkA9ytwsMQYo1ZJiR2zWIvSa5EmghjMOONmnBebPqqa2ZyKkgxks65VCmVUwp-oxWMVUtOJ10eRvTcPzW-KDZyrS-kUWKdpRAuKSioAXHk894l8hBonM3GFGbOJFo46moBWfN9s4M8dMP9_7Ueh-WQzofVULjASyUw5E7hCX7XvaL4VF1mD8AHxXsvw priority: 102 providerName: Springer Nature
Title	A bundle-free implicit programming approach for a class of elliptic MPECs in function space
URI	https://link.springer.com/article/10.1007/s10107-016-0983-9 https://www.proquest.com/docview/1827074931 https://www.proquest.com/docview/1845808693
Volume	160
WOSCitedRecordID	wos000385191700010&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: PRVPQU databaseName: ABI/INFORM Collection customDbUrl: eissn: 1436-4646 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0001388 issn: 0025-5610 databaseCode: 7WY dateStart: 20011001 isFulltext: true titleUrlDefault: https://www.proquest.com/abicomplete providerName: ProQuest – providerCode: PRVPQU databaseName: ABI/INFORM Global customDbUrl: eissn: 1436-4646 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0001388 issn: 0025-5610 databaseCode: M0C dateStart: 20011001 isFulltext: true titleUrlDefault: https://search.proquest.com/abiglobal providerName: ProQuest – providerCode: PRVPQU databaseName: Advanced Technologies & Aerospace Database customDbUrl: eissn: 1436-4646 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0001388 issn: 0025-5610 databaseCode: P5Z dateStart: 20011001 isFulltext: true titleUrlDefault: https://search.proquest.com/hightechjournals providerName: ProQuest – providerCode: PRVPQU databaseName: Computer Science Database customDbUrl: eissn: 1436-4646 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0001388 issn: 0025-5610 databaseCode: K7- dateStart: 20011001 isFulltext: true titleUrlDefault: http://search.proquest.com/compscijour providerName: ProQuest – providerCode: PRVPQU databaseName: Engineering Database customDbUrl: eissn: 1436-4646 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0001388 issn: 0025-5610 databaseCode: M7S dateStart: 20011001 isFulltext: true titleUrlDefault: http://search.proquest.com providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central - New (Subscription) customDbUrl: eissn: 1436-4646 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0001388 issn: 0025-5610 databaseCode: BENPR dateStart: 20011001 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVPQU databaseName: Science Database customDbUrl: eissn: 1436-4646 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0001388 issn: 0025-5610 databaseCode: M2P dateStart: 20011001 isFulltext: true titleUrlDefault: https://search.proquest.com/sciencejournals providerName: ProQuest – providerCode: PRVAVX databaseName: SpringerLINK Contemporary 1997-Present customDbUrl: eissn: 1436-4646 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0001388 issn: 0025-5610 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/eLvHCXMwpV1LbxMxEB71wQEOUB4VgRK5EieQRfYl2ydUolRIbaJVXxQ4rOxZW4oEm5JN-P3MbHaTgkQvvXhlrb1eaeyZz57xNwBvnQkxlmilRkTJjjPpMqVkWpaKrJF1ceM9vzpVk4m-vjZ5e-BWt2GVnU5sFHU5Qz4j_0A4WJG5M0n08eaX5KxR7F1tU2hswy4hm4hDusZxvtbEUaJ1l7KVcULn1VxdnYuaoEvaTxudSPO3XdqAzX_8o43ZOX5y3x_eg8ct4BRHqxnyFLZ89Qwe3aIhpNp4zd1aP4fvR8ItmXpBhrn3YtqEnE8Xoo3k-kldRMdELgjyCiuQIbiYBcHsnqSDUIzz0bAW00qw3WTZC9Jc6F_A5fHoYvhZtikYJCapWcjUmyRk3qR8k98ZnZYq0MNpF6MOIY1KdJpQ4cBYj9bqMliVlXHGtPm08Y6TfdipZpV_CYKgCzrerrEzNkqDZW0TWaWcp46Y9WDQCaDAlp-c02T8KDbMyiyzgmPSWGaF6cG7dZebFTnHXY0POjkV7Tqti42QenC4fk0rjN0mtvKzJbdJM007P5P04H03G2594n8Dvrp7wNfwMObp19xrPICdxXzp38AD_L2Y1vM-bKsvX_uw-2k0yc-odqIklePBsN9McS7VOZV59o3Ks_OrP_MK_rY
linkProvider	ProQuest
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1NT9wwEB0hitRyKPRLbAvUldpLK6skcWT7gBCiIBC7qz3QCqmH1HZsaaU2Sze7rfhT_MbOZONdigQ3DpyiKHaixM_PM5nxG4D3VofUlc5w5ZzjFDjjNpeSi7KUuBoZmzbR829d2e-r83M9WIKruBeG0iojJzZEXY4c_SP_jHawxOVOZ8nexW9OVaMouhpLaMxgceov_6LLVu-efMHx_ZCmR4dnB8e8rSrAXSb0hAuvs5B7LWhzutVKlDLgwSqbOhWCSEpnFRo6O9p4Z4wqg5F5meakBI--JAkdIOU_EqQsRqmC6WDO_EmmVCwRS3ZJjKLOtuolTZIn-u9aZVz_vw4ujNsb8dhmmTtae2gfaB2etgY125_NgGew5KvnsHpNZhHPenNt2voFfN9ndkrSEjyMvWfDJqV-OGFtptov7MKi0jpDk54Z5sjFYKPASL0UOdax3uDwoGbDipFdQNhmyMzOv4Sv9_Kur2C5GlV-AxiaZs6SO0rB5kQEQ2yaGCmtx44u78BOHPDCtfrrVAbkZ7FQjiaMFJRzRxgpdAc-zrtczMRH7mq8GXFRtDxUFwtQdODd_DIyCIWFTOVHU2ojcoWerc468Cmi79otbnvg67sf-BYeH5_1ukX3pH_6Bp6kBP1mD-cmLE_GU78FK-7PZFiPt5tJxODHfYPyH070VFs
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LS8QwEB58IXrwLa7PCJ6UsLZNSXIUdVHUZcEHgoeSpAksaFe2XX-_mW67rqKCeCqlSVsyycw3zMw3AAdautCkRlFhjKEYOKM65pyyNOXeGikdltHzh2vebovHR9mp-pzmdbZ7HZIc1jQgS1NWNF9T1xwrfAvKlEnvDUsRUTkJ0wzz6NFdv30YqeIgEqLu2YpAoQ5rfveKz4bpA21-CZCWdqe1-O8_XoKFCnKSk-EeWYYJm63A_BgRob-7GbG35qvwdEL0AMkXqOtbS7pl0nm3IFUu14ufQmoucuJBL1HEIAgnPUeQ39NrIUNuOuenOelmBC0nSp943WXsGty3zu9OL2jVhIGaiMmCMisjF1vJsJZfS8FS7vxFCx0a4RwLUqOFx4XHUlmjlEid4nEaxkic713vMFqHqayX2Q0gHrwYjQ4bhmMD5hTqm0Bxrq2faOIGHNcSSEzFUI6NMp6TD25lXMUEs9JwFRPZgMPRlNchPcdvg7drsSbVSc0T719xD6NkFDRgf_TYnzEMnKjM9gY4hsXC-34yasBRLeqxV_z0wc0_jd6D2c5ZK7m-bF9twVyIW6WsedyGqaI_sDswY96Kbt7fLff4O20L-Ic
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=A+bundle-free+implicit+programming+approach+for+a+class+of+elliptic+MPECs+in+function+space&rft.jtitle=Mathematical+programming&rft.au=Hinterm%C3%BCller%2C+M&rft.au=Surowiec%2C+T&rft.date=2016-11-01&rft.pub=Springer+Nature+B.V&rft.issn=0025-5610&rft.eissn=1436-4646&rft.volume=160&rft.issue=1-2&rft.spage=271&rft_id=info:doi/10.1007%2Fs10107-016-0983-9&rft.externalDocID=4208498161
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0025-5610&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0025-5610&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0025-5610&client=summon