A dual gradient-projection method for large-scale strictly convex quadratic problems

The details of a solver for minimizing a strictly convex quadratic objective function subject to general linear constraints are presented. The method uses a gradient projection algorithm enhanced with subspace acceleration to solve the bound-constrained dual optimization problem. Such gradient proje...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Computational optimization and applications Jg. 67; H. 1; S. 1 - 38
Hauptverfasser:	Gould, Nicholas I. M., Robinson, Daniel P.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York Springer US 01.05.2017 Springer Nature B.V
Schlagworte:	Acceleration Algorithms Computation Computer science Convex and Discrete Geometry Lagrange multiplier Linear algebra Management Science Mathematical analysis Mathematical models Mathematics Mathematics and Statistics Methods Operations Research Operations Research/Decision Theory Optimization Projection Quadratic programming Software packages Statistics Studies Gradient projection Large-scale optimization Sparse factorizations Quadratic programming Convex optimization Dual method
ISSN:	0926-6003, 1573-2894
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Abstract	The details of a solver for minimizing a strictly convex quadratic objective function subject to general linear constraints are presented. The method uses a gradient projection algorithm enhanced with subspace acceleration to solve the bound-constrained dual optimization problem. Such gradient projection methods are well-known, but are typically employed to solve the primal problem when only simple bound-constraints are present. The main contributions of this work are threefold. First, we address the challenges associated with solving the dual problem, which is usually a convex problem even when the primal problem is strictly convex. In particular, for the dual problem, one must efficiently compute directions of infinite descent when they exist, which is precisely when the primal formulation is infeasible. Second, we show how the linear algebra may be arranged to take computational advantage of sparsity that is often present in the second-derivative matrix, mostly by showing how sparse updates may be performed for algorithmic quantities. We consider the case that the second-derivative matrix is explicitly available and sparse, and the case when it is available implicitly via a limited memory BFGS representation. Third, we present the details of our Fortran 2003 software package DQP, which is part of the GALAHAD suite of optimization routines. Numerical tests are performed on quadratic programming problems from the combined CUTEst and Maros and Meszaros test sets.
AbstractList	The details of a solver for minimizing a strictly convex quadratic objective function subject to general linear constraints are presented. The method uses a gradient projection algorithm enhanced with subspace acceleration to solve the bound-constrained dual optimization problem. Such gradient projection methods are well-known, but are typically employed to solve the primal problem when only simple bound-constraints are present. The main contributions of this work are threefold. First, we address the challenges associated with solving the dual problem, which is usually a convex problem even when the primal problem is strictly convex. In particular, for the dual problem, one must efficiently compute directions of infinite descent when they exist, which is precisely when the primal formulation is infeasible. Second, we show how the linear algebra may be arranged to take computational advantage of sparsity that is often present in the second-derivative matrix, mostly by showing how sparse updates may be performed for algorithmic quantities. We consider the case that the second-derivative matrix is explicitly available and sparse, and the case when it is available implicitly via a limited memory BFGS representation. Third, we present the details of our Fortran 2003 software package DQP, which is part of the GALAHAD suite of optimization routines. Numerical tests are performed on quadratic programming problems from the combined CUTEst and Maros and Meszaros test sets. The details of a solver for minimizing a strictly convex quadratic objective function subject to general linear constraints are presented. The method uses a gradient projection algorithm enhanced with subspace acceleration to solve the bound-constrained dual optimization problem. Such gradient projection methods are well-known, but are typically employed to solve the primal problem when only simple bound-constraints are present. The main contributions of this work are threefold. First, we address the challenges associated with solving the dual problem, which is usually a convex problem even when the primal problem is strictly convex. In particular, for the dual problem, one must efficiently compute directions of infinite descent when they exist, which is precisely when the primal formulation is infeasible. Second, we show how the linear algebra may be arranged to take computational advantage of sparsity that is often present in the second-derivative matrix, mostly by showing how sparse updates may be performed for algorithmic quantities. We consider the case that the second-derivative matrix is explicitly available and sparse, and the case when it is available implicitly via a limited memory BFGS representation. Third, we present the details of our Fortran 2003 software package DQP, which is part of the GALAHAD suite of optimization routines. Numerical tests are performed on quadratic programming problems from the combined CUTEst and Maros and Meszaros test sets.
Author	Gould, Nicholas I. M. Robinson, Daniel P.
Author_xml	– sequence: 1 givenname: Nicholas I. M. surname: Gould fullname: Gould, Nicholas I. M. organization: Scientific Computing Department, STFC-Rutherford Appleton Laboratory – sequence: 2 givenname: Daniel P. orcidid: 0000-0003-0251-4227 surname: Robinson fullname: Robinson, Daniel P. email: daniel.p.robinson@gmail.com organization: Department of Applied Mathematics and Statistics, The Johns Hopkins University
BookMark	eNp9kLFqHDEQhkVwIGfHD5BOkCaN7NFKp5VKY2I7YEhzqYVWOzrvoVudJW2I3946LkUwxNU03zfzz39OzuY0IyFfOFxxgP66cFhrw4ArZrRWjH8gK77uBeu0kWdkBaZTTAGIT-S8lB0AmF50K7K5oePiIt1mN044V3bIaYe-Tmmme6xPaaQhZRpd3iIr3kWkpebJ1_hCfZp_4x_6vLgxuzp52twh4r58Jh-DiwUv_84L8uvu--b2gT3-vP9xe_PIvJCmsiGAVzj03jkIHUqOvZDBjaK94kKvZB8GULLjg5GD0oqrtVhz8FoF7rlEcUG-nfa2w88Llmr3U_EYo5sxLcVybYQBAZI39OsbdJeWPLd0jdKgNLRIjepPlM-plIzB-qm6Yxk1uylaDvbYtj21bVvb9ti2Pe7nb8xDnvYuv7zrdCenNHbeYv4n03-lV40Pk84
CitedBy_id	crossref_primary_10_1007_s11075_017_0467_x crossref_primary_10_1007_s12532_018_0147_4 crossref_primary_10_1016_j_ast_2024_108937
Cites_doi	10.1007/BF02592073 10.1155/S1110757X04309071 10.1007/s10589-014-9687-3 10.1007/BF02192216 10.1137/130918320 10.1093/imanum/drq043 10.1016/0098-1354(94)E0001-4 10.1080/10556789908805758 10.1145/992200.992202 10.1007/BF01582063 10.1007/BF00935003 10.1080/10556789908805768 10.1137/140996677 10.1007/BF02591962 10.1137/080744542 10.1137/1033001 10.1007/s10589-005-4557-7 10.1007/s11075-006-9019-5 10.1090/qam/112751 10.1137/0801008 10.1137/1.9781611971484 10.1137/S1052623401383558 10.1145/962437.962438 10.1145/1499096.1499098 10.1137/1.9780898719857 10.1016/0024-3795(91)90009-L 10.1145/356044.356047 10.1007/BF02614503 10.1017/S0962492900002518 10.1007/s12532-012-0050-3 10.1080/10556789908805759 10.1007/BF01584341 10.4236/am.2010.11002 10.1007/s11081-006-6588-z 10.1016/S0168-9274(02)00120-4 10.1017/S0962492904000212 10.1137/130920599 10.1137/0728026 10.1090/S0025-5718-1988-0929544-3 10.1145/192115.192132 10.1137/060669930 10.1093/imanum/drq037 10.1137/110845094 10.1007/s12532-012-0035-2 10.1137/0803039 10.1007/BF00248762 10.1007/978-1-4613-0263-6_8 10.1137/080744554 10.1137/0721072 10.1137/15M1022100 10.1137/090757216 10.1093/oso/9780198535645.003.0008 10.1007/s11590-012-0476-6 10.1007/s10589-014-9681-9 10.1145/512274.512284 10.1109/CDC.2008.4738961 10.1007/s10107-015-0966-2 10.1007/978-0-387-35514-6_7
ContentType	Journal Article
Copyright	Springer Science+Business Media New York 2016 Computational Optimization and Applications is a copyright of Springer, 2017.
Copyright_xml	– notice: Springer Science+Business Media New York 2016 – notice: Computational Optimization and Applications is a copyright of Springer, 2017.
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.- 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/s10589-016-9886-1
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 Collection 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 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 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 (UW System Shared) 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 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	ProQuest Business Collection (Alumni Edition) Computer and Information Systems Abstracts
Database_xml	– sequence: 1 dbid: BENPR name: ProQuest Central url: https://www.proquest.com/central sourceTypes: Aggregation Database
DeliveryMethod	fulltext_linktorsrc
Discipline	Engineering Statistics Mathematics Computer Science
EISSN	1573-2894
EndPage	38
ExternalDocumentID	4321147113 10_1007_s10589_016_9886_1
Genre	Feature
GrantInformation_xml	– fundername: Engineering and Physical Sciences Research Council grantid: EP/I013067/1 funderid: http://dx.doi.org/10.13039/501100000266
GroupedDBID	-52 -5D -5G -BR -EM -Y2 -~C .4S .86 .DC .VR 06D 0R~ 0VY 1N0 1SB 2.D 203 28- 29F 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2~H 30V 3V. 4.4 406 408 409 40D 40E 5GY 5QI 5VS 67Z 6NX 7WY 88I 8AO 8FE 8FG 8FL 8FW 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 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 ACOKC ACOMO ACPIV ACSNA ACZOJ ADHHG ADHIR ADINQ ADKNI ADKPE ADMLS ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFEXP AFGCZ AFKRA AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHQJS AHSBF AHYZX AI. 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-. BA0 BAPOH BBWZM BDATZ BENPR BEZIV BGLVJ BGNMA BPHCQ BSONS CAG CCPQU COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP DU5 DWQXO EBLON EBS EBU EDO EIOEI EJD ESBYG F5P 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 GXS H13 HCIFZ HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I-F I09 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 LAK LLZTM M0C M0N M2P M4Y M7S MA- N2Q N9A NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM OVD P19 P2P P62 P9R PF0 PQBIZ PQBZA PQQKQ PROAC PT4 PT5 PTHSS Q2X QOK QOS QWB R4E R89 R9I RHV RNI RNS ROL RPX RSV RZC RZD 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 TEORI TH9 TN5 TSG TSK TSV TUC TUS U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW VH1 W23 W48 WK8 YLTOR Z45 Z7R Z7S Z7X Z81 Z83 Z86 Z88 Z8M Z8N Z8R Z8U Z8W Z92 ZL0 ZMTXR ZWQNP ~8M ~EX AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC ADHKG AEZWR AFDZB AFFHD AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP AMVHM ATHPR AYFIA CITATION PHGZM PHGZT PQGLB 7SC 7XB 8AL 8FD 8FK JQ2 L.- L7M L~C L~D PKEHL PQEST PQUKI PRINS Q9U PUEGO
ID	FETCH-LOGICAL-c349t-bf0c6eb7caa0f2e41e734fad3058af7647fb06421b94b6861653510c86f1c14e3
IEDL.DBID	RSV
ISICitedReferencesCount	3
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000398939500001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	0926-6003
IngestDate	Sun Aug 24 03:26:21 EDT 2025 Wed Nov 26 14:51:48 EST 2025 Tue Nov 18 20:12:49 EST 2025 Sat Nov 29 01:51:28 EST 2025 Fri Feb 21 02:30:34 EST 2025
IsPeerReviewed	true
IsScholarly	true
Issue	1
Keywords	Gradient projection Large-scale optimization Sparse factorizations Quadratic programming Convex optimization Dual method
Language	English
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c349t-bf0c6eb7caa0f2e41e734fad3058af7647fb06421b94b6861653510c86f1c14e3
Notes	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-1 ObjectType-Feature-2 content type line 23
ORCID	0000-0003-0251-4227
PQID	1880680349
PQPubID	30811
PageCount	38
ParticipantIDs	proquest_miscellaneous_1893903041 proquest_journals_1880680349 crossref_citationtrail_10_1007_s10589_016_9886_1 crossref_primary_10_1007_s10589_016_9886_1 springer_journals_10_1007_s10589_016_9886_1
PublicationCentury	2000
PublicationDate	20170500 2017-5-00 20170501
PublicationDateYYYYMMDD	2017-05-01
PublicationDate_xml	– month: 5 year: 2017 text: 20170500
PublicationDecade	2010
PublicationPlace	New York
PublicationPlace_xml	– name: New York
PublicationSubtitle	An International Journal
PublicationTitle	Computational optimization and applications
PublicationTitleAbbrev	Comput Optim Appl
PublicationYear	2017
Publisher	Springer US Springer Nature B.V
Publisher_xml	– name: Springer US – name: Springer Nature B.V
References	Gould, Toint, Siddiqi, Kočvara (CR43) 2002 Calamai, Moré (CR12) 1987; 39 Gould, Orban, Toint (CR39) 2015; 60 CR34 Friedlander, Orban (CR30) 2012; 4 Duff (CR24) 2004; 30 CR72 Gould, Robinson (CR47) 2010; 20 Bierlaire, Toint, Tuyttens (CR6) 1991; 143 Gould, Loh, Robinson (CR44) 2014; 24 Gill, Murray, Saunders, Wright (CR33) 1991; 33 Gould, Toint (CR42) 2002; 43 Gould, Loh, Robinson (CR45) 2015; 25 Gill, Murray, Saunders, Wright, Cox, Hammarling (CR35) 1990 CR2 Curtis, Johnson, Robinson, Wachter (CR19) 2014; 24 Vanderbei (CR74) 1999; 11 Dorn (CR21) 1960; 18 Hogg, Reid, Scott (CR53) 2010; 32 Bisschop, Meeraus (CR7) 1977; 13 CR49 Schmid, Biegler (CR71) 1994; 18 Byrd, Nocedal, Schnabel (CR11) 1994; 63 Gould, Toint, Powell, Scholtes (CR41) 2000 Boggs, Tolle (CR9) 1995; 4 Lancaster, Tismenetsky (CR57) 1985 Gill, Murray, Saunders, Wright, Cox, Hammarling (CR32) 1990 George, Liu (CR31) 1981 CR40 Friedlander, Leyffer (CR29) 2008; 30 Conn, Gould (CR13) 1984; 21 Yuan, Lu, Wei (CR76) 2010; 1 Moyh-ud Din, Robinson (CR64) 2015; 25 Conn, Gould, Toint (CR16) 2000 Moré, Thuente (CR63) 1994; 20 CR18 Zhu, Rockafellar (CR77) 1993; 3 CR17 Duff, Reid (CR25) 1983; 9 Hintermüller, Kunisch (CR52) 2002; 13 CR14 Björck (CR8) 1996 Fletcher, Boggs, Byrd, Schnabel (CR26) 1985 CR56 CR55 Lescrenier (CR58) 1991; 28 Nocedal, Wright (CR65) 2006 CR54 Dostál, Schöberl (CR23) 2005; 30 Morales, Nocedal, Wu (CR61) 2012; 32 CR50 Moré, Toraldo (CR62) 1991; 1 Schenk, Gärtner (CR70) 2006; 23 Boland (CR10) 1997; 78 Conn, Gould, Toint (CR15) 1988; 50 Hager, Hearn (CR51) 1993; 1 Benzi, Golub, Liesen (CR4) 2005; 14 Arioli, Laratta, Menchi (CR1) 1984; 43 Stefanov (CR73) 2004; 2004 Goldfarb, Idnani (CR36) 1983; 27 Bartlett, Biegler (CR3) 2006; 7 Betts, Frank (CR5) 1994; 82 CR28 Dostál (CR22) 2009 CR27 Maros, Meszaros (CR59) 1999; 11–12 CR67 CR66 Gould, Robinson (CR46) 2010; 20 Dominguez, González-Lima (CR20) 2006; 42 Gould, Robinson (CR48) 2012; 32 Williams (CR75) 1964; 7 Gould, Orban, Toint (CR38) 2003; 29 Mészáros (CR60) 1999; 11 Reid, Scott (CR68) 2009; 36 Robinson, Feng, Nocedal, Pang (CR69) 2013; 23 Gould, Orban, Robinson (CR37) 2013; 5 NIM Gould (9886_CR44) 2014; 24 JT Betts (9886_CR5) 1994; 82 M Hintermüller (9886_CR52) 2002; 13 P Lancaster (9886_CR57) 1985 M Arioli (9886_CR1) 1984; 43 M Bierlaire (9886_CR6) 1991; 143 MP Friedlander (9886_CR30) 2012; 4 C Schmid (9886_CR71) 1994; 18 NIM Gould (9886_CR41) 2000 9886_CR49 H Moyh-ud Din (9886_CR64) 2015; 25 R Fletcher (9886_CR26) 1985 M Lescrenier (9886_CR58) 1991; 28 NIM Gould (9886_CR37) 2013; 5 NIM Gould (9886_CR39) 2015; 60 9886_CR40 Å Björck (9886_CR8) 1996 DP Robinson (9886_CR69) 2013; 23 C Mészáros (9886_CR60) 1999; 11 SM Stefanov (9886_CR73) 2004; 2004 AR Conn (9886_CR13) 1984; 21 AR Conn (9886_CR15) 1988; 50 9886_CR18 9886_CR56 9886_CR55 PE Gill (9886_CR32) 1990 9886_CR54 9886_CR17 RH Byrd (9886_CR11) 1994; 63 WW Hager (9886_CR51) 1993; 1 JL Morales (9886_CR61) 2012; 32 9886_CR14 JJ Moré (9886_CR62) 1991; 1 W Dorn (9886_CR21) 1960; 18 Z Dostál (9886_CR22) 2009 J Bisschop (9886_CR7) 1977; 13 9886_CR50 PE Gill (9886_CR35) 1990 M Benzi (9886_CR4) 2005; 14 JK Reid (9886_CR68) 2009; 36 MP Friedlander (9886_CR29) 2008; 30 IS Duff (9886_CR24) 2004; 30 NL Boland (9886_CR10) 1997; 78 Z Dostál (9886_CR23) 2005; 30 NIM Gould (9886_CR47) 2010; 20 9886_CR67 9886_CR66 9886_CR28 9886_CR27 C Zhu (9886_CR77) 1993; 3 NIM Gould (9886_CR45) 2015; 25 NIM Gould (9886_CR42) 2002; 43 RA Bartlett (9886_CR3) 2006; 7 NIM Gould (9886_CR43) 2002 PH Calamai (9886_CR12) 1987; 39 I Maros (9886_CR59) 1999; 11–12 AR Conn (9886_CR16) 2000 J Dominguez (9886_CR20) 2006; 42 D Goldfarb (9886_CR36) 1983; 27 JD Hogg (9886_CR53) 2010; 32 A George (9886_CR31) 1981 RJ Vanderbei (9886_CR74) 1999; 11 O Schenk (9886_CR70) 2006; 23 NIM Gould (9886_CR46) 2010; 20 9886_CR34 NIM Gould (9886_CR38) 2003; 29 JWJ Williams (9886_CR75) 1964; 7 G Yuan (9886_CR76) 2010; 1 IS Duff (9886_CR25) 1983; 9 PE Gill (9886_CR33) 1991; 33 J Nocedal (9886_CR65) 2006 JJ Moré (9886_CR63) 1994; 20 9886_CR2 FE Curtis (9886_CR19) 2014; 24 9886_CR72 PT Boggs (9886_CR9) 1995; 4 NIM Gould (9886_CR48) 2012; 32
References_xml	– volume: 39 start-page: 93 issue: 1 year: 1987 end-page: 116 ident: CR12 article-title: Projected gradient methods for linearly constrained problems publication-title: Math. Program. doi: 10.1007/BF02592073 – volume: 2004 start-page: 409 issue: 5 year: 2004 end-page: 431 ident: CR73 article-title: Polynomial algorithms for projecting a point onto a region defined by a linear constraint and box constraints in publication-title: J. Appl. Math. doi: 10.1155/S1110757X04309071 – volume: 60 start-page: 545 issue: 3 year: 2015 end-page: 557 ident: CR39 article-title: CUTEst: a constrained and unconstrained testing environment with safe threads for mathematical optimization publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-014-9687-3 – volume: 82 start-page: 519 year: 1994 end-page: 541 ident: CR5 article-title: A sparse nonlinear optimization algorithm publication-title: J. Optim. Theory Appl. doi: 10.1007/BF02192216 – start-page: 26 year: 1985 end-page: 40 ident: CR26 article-title: An penalty method for nonlinear constraints publication-title: Numerical Optimization 1984 – volume: 24 start-page: 1041 issue: 3 year: 2014 end-page: 1074 ident: CR19 article-title: An inexact sequential quadratic optimization algorithm for nonlinear optimization publication-title: SIAM J. Optim. doi: 10.1137/130918320 – volume: 32 start-page: 580 issue: 2 year: 2012 end-page: 601 ident: CR48 article-title: A second derivative SQP method with a ‘trust-region-free’ predictor step publication-title: IMA J. Numer. Anal. doi: 10.1093/imanum/drq043 – ident: CR49 – volume: 18 start-page: 817 issue: 9 year: 1994 end-page: 832 ident: CR71 article-title: Quadratic programming methods for reduced hessian sqp publication-title: Comput. Chem. Eng. doi: 10.1016/0098-1354(94)E0001-4 – year: 1985 ident: CR57 publication-title: The Theory of Matrices: With Applications – volume: 11 start-page: 431 issue: 1–4 year: 1999 end-page: 449 ident: CR60 article-title: The BPMPD interior point solver for convex quadratic problems publication-title: Optim. Methods Softw. doi: 10.1080/10556789908805758 – volume: 30 start-page: 118 issue: 2 year: 2004 end-page: 144 ident: CR24 article-title: MA57—a code for the solution of sparse symmetric definite and indefinite systems publication-title: ACM Trans. Math. Softw. doi: 10.1145/992200.992202 – volume: 63 start-page: 129 issue: 2 year: 1994 end-page: 156 ident: CR11 article-title: Representations of quasi-Newton matrices and their use in limited memory methods publication-title: Math. Program. doi: 10.1007/BF01582063 – volume: 43 start-page: 495 issue: 4 year: 1984 end-page: 525 ident: CR1 article-title: Numerical computation of the projection of a point onto a polyhedron publication-title: J. Optim. Theory Appl. doi: 10.1007/BF00935003 – volume: 11–12 start-page: 671 year: 1999 end-page: 681 ident: CR59 article-title: A repository of convex quadratic programming problems publication-title: Optim. Methods Softw. doi: 10.1080/10556789908805768 – ident: CR54 – volume: 25 start-page: 1885 issue: 3 year: 2015 end-page: 1911 ident: CR45 article-title: A filter SQP method: local convergence and numerical results publication-title: SIAM J. Optim. doi: 10.1137/140996677 – volume: 27 start-page: 1 issue: 1 year: 1983 end-page: 33 ident: CR36 article-title: A numerically stable dual method for solving strictly convex quadratic programs publication-title: Math. Program. doi: 10.1007/BF02591962 – volume: 20 start-page: 2023 issue: 4 year: 2010 end-page: 2048 ident: CR46 article-title: A second derivative SQP method: global convergence publication-title: SIAM J. Optim. doi: 10.1137/080744542 – volume: 33 start-page: 1 issue: 1 year: 1991 end-page: 36 ident: CR33 article-title: Inertia-controlling methods for general quadratic programming publication-title: SIAM Rev. doi: 10.1137/1033001 – volume: 30 start-page: 23 issue: 1 year: 2005 end-page: 43 ident: CR23 article-title: Minimizing quadratic functions subject to bound constraints with the rate of convergence and finite termination publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-005-4557-7 – volume: 42 start-page: 1 issue: 1 year: 2006 end-page: 30 ident: CR20 article-title: A primal-dual interior-point algorithm for quadratic programming publication-title: Numer. Algorithms doi: 10.1007/s11075-006-9019-5 – ident: CR67 – volume: 18 start-page: 155 year: 1960 end-page: 162 ident: CR21 article-title: Duality in quadratic programming publication-title: Q. Appl. Math. doi: 10.1090/qam/112751 – ident: CR50 – volume: 1 start-page: 93 issue: 1 year: 1991 end-page: 113 ident: CR62 article-title: On the solution of large quadratic programming problems with bound constraints publication-title: SIAM J. Optim. doi: 10.1137/0801008 – year: 1996 ident: CR8 publication-title: Numerical Methods for Least Squares Problems doi: 10.1137/1.9781611971484 – volume: 13 start-page: 865 issue: 3 year: 2002 end-page: 888 ident: CR52 article-title: The primal-dual active set strategy as a semismooth Newton method publication-title: SIAM J. Optim. doi: 10.1137/S1052623401383558 – volume: 23 start-page: 158 year: 2006 end-page: 179 ident: CR70 article-title: On fast factorization pivoting methods for symmetric indefinite systems publication-title: Electron. Trans. Numer. Anal. – year: 2006 ident: CR65 publication-title: Numerical Optimization – year: 1981 ident: CR31 publication-title: Computer Solution of Large Sparse Positive Definite Systems – volume: 29 start-page: 353 issue: 4 year: 2003 end-page: 372 ident: CR38 article-title: GALAHAD—a library of thread-safe fortran 90 packages for large-scale nonlinear optimization publication-title: ACM Trans. Math. Softw. doi: 10.1145/962437.962438 – volume: 36 start-page: 9 issue: 2 year: 2009 ident: CR68 article-title: An out-of-core sparse Cholesky solver publication-title: ACM Trans. Math. Softw. doi: 10.1145/1499096.1499098 – year: 2000 ident: CR16 publication-title: Trust-Region Methods doi: 10.1137/1.9780898719857 – ident: CR18 – volume: 143 start-page: 111 year: 1991 end-page: 143 ident: CR6 article-title: On iterative algorithms for linear least squares problems with bound constraints publication-title: Linear Algebra Appl. doi: 10.1016/0024-3795(91)90009-L – ident: CR66 – volume: 9 start-page: 302 issue: 3 year: 1983 end-page: 325 ident: CR25 article-title: The multifrontal solution of indefinite sparse symmetric linear equations publication-title: ACM Trans. Math. Softw. doi: 10.1145/356044.356047 – ident: CR72 – volume: 78 start-page: 1 issue: 1 year: 1997 end-page: 27 ident: CR10 article-title: A dual-active-set algorithm for positive semi-definite quadratic programming publication-title: Math. Program. Ser. A doi: 10.1007/BF02614503 – ident: CR14 – ident: CR2 – volume: 4 start-page: 1 year: 1995 end-page: 51 ident: CR9 article-title: Sequential quadratic programming publication-title: Acta Numer. doi: 10.1017/S0962492900002518 – start-page: 113 year: 1990 end-page: 138 ident: CR35 article-title: A Schur-complement method for sparse quadratic programming publication-title: Reliable Numerical Computation – volume: 5 start-page: 113 issue: 2 year: 2013 end-page: 142 ident: CR37 article-title: Trajectory-following methods for large-scale degenerate convex quadratic programming publication-title: Math. Program. Comput. doi: 10.1007/s12532-012-0050-3 – volume: 11 start-page: 451 issue: 1–4 year: 1999 end-page: 484 ident: CR74 article-title: LOQO: an interior point code for quadratic programming publication-title: Optim. Methods Softw. doi: 10.1080/10556789908805759 – volume: 13 start-page: 241 issue: 3 year: 1977 end-page: 254 ident: CR7 article-title: Matrix augmentation and partitioning in the updating of the basis inverse publication-title: Math. Program. doi: 10.1007/BF01584341 – volume: 1 start-page: 8 issue: 1 year: 2010 end-page: 17 ident: CR76 article-title: A modified limited SQP method for constrained optimization publication-title: Appl. Math. doi: 10.4236/am.2010.11002 – start-page: 149 year: 2000 end-page: 178 ident: CR41 article-title: SQP methods for large-scale nonlinear programming publication-title: System Modelling and Optimization. Methods, Theory and Applications – ident: CR56 – ident: CR40 – ident: CR27 – volume: 7 start-page: 5 issue: 1 year: 2006 end-page: 32 ident: CR3 article-title: QPSchur: a dual, active-set, Schur-complement method for large-scale and structured convex quadratic programming publication-title: Optim. Eng. doi: 10.1007/s11081-006-6588-z – start-page: 113 year: 1990 end-page: 138 ident: CR32 article-title: A Schur-complement method for sparse quadratic programming publication-title: Reliable Scientific Computation – volume: 43 start-page: 109 issue: 1–2 year: 2002 end-page: 128 ident: CR42 article-title: An iterative working-set method for large-scale non-convex quadratic programming publication-title: Appl. Numer. Math. doi: 10.1016/S0168-9274(02)00120-4 – volume: 14 start-page: 1 year: 2005 end-page: 137 ident: CR4 article-title: Numerical solution of saddle point problems publication-title: Acta Numer. doi: 10.1017/S0962492904000212 – volume: 24 start-page: 175 issue: 1 year: 2014 end-page: 209 ident: CR44 article-title: A filter method with unified step computation for nonlinear optimization publication-title: SIAM J. Optim. doi: 10.1137/130920599 – ident: CR17 – volume: 28 start-page: 476 issue: 2 year: 1991 end-page: 495 ident: CR58 article-title: Convergence of trust region algorithms for optimization with bounds when strict complementarity does not hold publication-title: SIAM J. Numer. Anal. doi: 10.1137/0728026 – volume: 50 start-page: 399 year: 1988 end-page: 430 ident: CR15 article-title: Testing a class of methods for solving minimization problems with simple bounds on the variables publication-title: Math. Comput. doi: 10.1090/S0025-5718-1988-0929544-3 – volume: 20 start-page: 286 issue: 3 year: 1994 end-page: 307 ident: CR63 article-title: Line search algorithms with guaranteed sufficient decrease publication-title: ACM Trans. Math. Softw. doi: 10.1145/192115.192132 – volume: 30 start-page: 1706 issue: 4 year: 2008 end-page: 1729 ident: CR29 article-title: Global and finite termination of a two-phase augmented Lagrangian filter method for general quadratic programs publication-title: SIAM J. Sci. Comput. doi: 10.1137/060669930 – volume: 32 start-page: 553 year: 2012 end-page: 579 ident: CR61 article-title: A sequential quadratic programming algorithm with an additional equality constrained phase publication-title: IMA J. Numer. Anal. doi: 10.1093/imanum/drq037 – volume: 23 start-page: 1371 issue: 3 year: 2013 end-page: 1397 ident: CR69 article-title: Subspace accelerated matrix splitting algorithms for asymmetric and symmetric linear complementarity problems publication-title: SIAM J. Optim. doi: 10.1137/110845094 – volume: 4 start-page: 71 issue: 1 year: 2012 end-page: 107 ident: CR30 article-title: A primal-dual regularized interior-point method for convex quadratic programs publication-title: Math. Program. Comput. doi: 10.1007/s12532-012-0035-2 – ident: CR34 – volume: 3 start-page: 751 issue: 4 year: 1993 end-page: 783 ident: CR77 article-title: Primal-dual projected gradient algorithms for extended linear-quadratic programming publication-title: SIAM J. Optim. doi: 10.1137/0803039 – volume: 1 start-page: 349 issue: 4 year: 1993 end-page: 373 ident: CR51 article-title: Application of the dual active set algorithm to quadratic network optimization publication-title: Comput. Optim. Appl. doi: 10.1007/BF00248762 – ident: CR55 – start-page: 149 year: 2002 end-page: 179 ident: CR43 article-title: Numerical methods for large-scale non-convex quadratic programming publication-title: Trends in Industrial and Applied Mathematics doi: 10.1007/978-1-4613-0263-6_8 – volume: 20 start-page: 2049 issue: 4 year: 2010 end-page: 2079 ident: CR47 article-title: A second derivative SQP method: local convergence and practical issues publication-title: SIAM J. Optim. doi: 10.1137/080744554 – year: 2009 ident: CR22 publication-title: Optimal Quadratic Programming Algorithms: With Applications to Variational Inequalities – ident: CR28 – volume: 21 start-page: 302 issue: 6 year: 1984 end-page: 325 ident: CR13 article-title: On the location of directions of infinite descent for nonlinear programming algorithms publication-title: SIAM J. Numer. Anal. doi: 10.1137/0721072 – volume: 25 start-page: 2385 issue: 4 year: 2015 end-page: 2407 ident: CR64 article-title: A solver for nonconvex bound-constrained quadratic optimization publication-title: SIAM J. Optim. doi: 10.1137/15M1022100 – volume: 7 start-page: 347 year: 1964 end-page: 348 ident: CR75 article-title: Algorithm 232. Heapsort publication-title: Commun. ACM – volume: 32 start-page: 36273649 issue: 6 year: 2010 ident: CR53 article-title: Design of a multicore sparse Cholesky factorization using DAGs publication-title: SIAM J. Sci. Comput. doi: 10.1137/090757216 – volume-title: Trust-Region Methods year: 2000 ident: 9886_CR16 doi: 10.1137/1.9780898719857 – start-page: 113 volume-title: Reliable Scientific Computation year: 1990 ident: 9886_CR32 doi: 10.1093/oso/9780198535645.003.0008 – volume: 78 start-page: 1 issue: 1 year: 1997 ident: 9886_CR10 publication-title: Math. Program. Ser. A doi: 10.1007/BF02614503 – ident: 9886_CR66 doi: 10.1007/s11590-012-0476-6 – volume: 18 start-page: 155 year: 1960 ident: 9886_CR21 publication-title: Q. Appl. Math. doi: 10.1090/qam/112751 – volume: 32 start-page: 553 year: 2012 ident: 9886_CR61 publication-title: IMA J. Numer. Anal. doi: 10.1093/imanum/drq037 – ident: 9886_CR18 doi: 10.1007/s10589-014-9681-9 – volume-title: Numerical Methods for Least Squares Problems year: 1996 ident: 9886_CR8 doi: 10.1137/1.9781611971484 – volume: 33 start-page: 1 issue: 1 year: 1991 ident: 9886_CR33 publication-title: SIAM Rev. doi: 10.1137/1033001 – volume: 7 start-page: 347 year: 1964 ident: 9886_CR75 publication-title: Commun. ACM doi: 10.1145/512274.512284 – volume: 29 start-page: 353 issue: 4 year: 2003 ident: 9886_CR38 publication-title: ACM Trans. Math. Softw. doi: 10.1145/962437.962438 – ident: 9886_CR49 – volume: 36 start-page: 9 issue: 2 year: 2009 ident: 9886_CR68 publication-title: ACM Trans. Math. Softw. – volume: 27 start-page: 1 issue: 1 year: 1983 ident: 9886_CR36 publication-title: Math. Program. doi: 10.1007/BF02591962 – volume: 143 start-page: 111 year: 1991 ident: 9886_CR6 publication-title: Linear Algebra Appl. doi: 10.1016/0024-3795(91)90009-L – volume: 20 start-page: 286 issue: 3 year: 1994 ident: 9886_CR63 publication-title: ACM Trans. Math. Softw. doi: 10.1145/192115.192132 – volume: 5 start-page: 113 issue: 2 year: 2013 ident: 9886_CR37 publication-title: Math. Program. Comput. doi: 10.1007/s12532-012-0050-3 – ident: 9886_CR56 – volume: 25 start-page: 2385 issue: 4 year: 2015 ident: 9886_CR64 publication-title: SIAM J. Optim. doi: 10.1137/15M1022100 – volume-title: Optimal Quadratic Programming Algorithms: With Applications to Variational Inequalities year: 2009 ident: 9886_CR22 – volume: 18 start-page: 817 issue: 9 year: 1994 ident: 9886_CR71 publication-title: Comput. Chem. Eng. doi: 10.1016/0098-1354(94)E0001-4 – ident: 9886_CR14 – volume: 2004 start-page: 409 issue: 5 year: 2004 ident: 9886_CR73 publication-title: J. Appl. Math. doi: 10.1155/S1110757X04309071 – volume: 25 start-page: 1885 issue: 3 year: 2015 ident: 9886_CR45 publication-title: SIAM J. Optim. doi: 10.1137/140996677 – volume: 11 start-page: 431 issue: 1–4 year: 1999 ident: 9886_CR60 publication-title: Optim. Methods Softw. doi: 10.1080/10556789908805758 – volume: 42 start-page: 1 issue: 1 year: 2006 ident: 9886_CR20 publication-title: Numer. Algorithms doi: 10.1007/s11075-006-9019-5 – volume: 1 start-page: 349 issue: 4 year: 1993 ident: 9886_CR51 publication-title: Comput. Optim. Appl. doi: 10.1007/BF00248762 – volume: 1 start-page: 8 issue: 1 year: 2010 ident: 9886_CR76 publication-title: Appl. Math. doi: 10.4236/am.2010.11002 – volume: 24 start-page: 1041 issue: 3 year: 2014 ident: 9886_CR19 publication-title: SIAM J. Optim. doi: 10.1137/130918320 – volume: 9 start-page: 302 issue: 3 year: 1983 ident: 9886_CR25 publication-title: ACM Trans. Math. Softw. doi: 10.1145/356044.356047 – volume: 50 start-page: 399 year: 1988 ident: 9886_CR15 publication-title: Math. Comput. doi: 10.1090/S0025-5718-1988-0929544-3 – volume: 21 start-page: 302 issue: 6 year: 1984 ident: 9886_CR13 publication-title: SIAM J. Numer. Anal. – volume: 30 start-page: 23 issue: 1 year: 2005 ident: 9886_CR23 publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-005-4557-7 – start-page: 113 volume-title: Reliable Numerical Computation year: 1990 ident: 9886_CR35 doi: 10.1093/oso/9780198535645.003.0008 – volume: 60 start-page: 545 issue: 3 year: 2015 ident: 9886_CR39 publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-014-9687-3 – volume: 11 start-page: 451 issue: 1–4 year: 1999 ident: 9886_CR74 publication-title: Optim. Methods Softw. doi: 10.1080/10556789908805759 – volume: 13 start-page: 865 issue: 3 year: 2002 ident: 9886_CR52 publication-title: SIAM J. Optim. doi: 10.1137/S1052623401383558 – ident: 9886_CR55 – ident: 9886_CR17 – ident: 9886_CR34 – volume: 28 start-page: 476 issue: 2 year: 1991 ident: 9886_CR58 publication-title: SIAM J. Numer. Anal. doi: 10.1137/0728026 – volume: 20 start-page: 2023 issue: 4 year: 2010 ident: 9886_CR46 publication-title: SIAM J. Optim. doi: 10.1137/080744542 – ident: 9886_CR72 – volume: 4 start-page: 71 issue: 1 year: 2012 ident: 9886_CR30 publication-title: Math. Program. Comput. doi: 10.1007/s12532-012-0035-2 – volume: 7 start-page: 5 issue: 1 year: 2006 ident: 9886_CR3 publication-title: Optim. Eng. doi: 10.1007/s11081-006-6588-z – ident: 9886_CR40 – volume: 30 start-page: 118 issue: 2 year: 2004 ident: 9886_CR24 publication-title: ACM Trans. Math. Softw. doi: 10.1145/992200.992202 – ident: 9886_CR67 – volume: 24 start-page: 175 issue: 1 year: 2014 ident: 9886_CR44 publication-title: SIAM J. Optim. doi: 10.1137/130920599 – volume: 32 start-page: 36273649 issue: 6 year: 2010 ident: 9886_CR53 publication-title: SIAM J. Sci. Comput. – volume: 39 start-page: 93 issue: 1 year: 1987 ident: 9886_CR12 publication-title: Math. Program. doi: 10.1007/BF02592073 – ident: 9886_CR28 – volume-title: The Theory of Matrices: With Applications year: 1985 ident: 9886_CR57 – volume: 23 start-page: 158 year: 2006 ident: 9886_CR70 publication-title: Electron. Trans. Numer. Anal. – volume-title: Numerical Optimization year: 2006 ident: 9886_CR65 – ident: 9886_CR50 – volume: 43 start-page: 109 issue: 1–2 year: 2002 ident: 9886_CR42 publication-title: Appl. Numer. Math. doi: 10.1016/S0168-9274(02)00120-4 – ident: 9886_CR2 doi: 10.1109/CDC.2008.4738961 – start-page: 26 volume-title: Numerical Optimization 1984 year: 1985 ident: 9886_CR26 – volume: 43 start-page: 495 issue: 4 year: 1984 ident: 9886_CR1 publication-title: J. Optim. Theory Appl. doi: 10.1007/BF00935003 – start-page: 149 volume-title: Trends in Industrial and Applied Mathematics year: 2002 ident: 9886_CR43 doi: 10.1007/978-1-4613-0263-6_8 – volume: 20 start-page: 2049 issue: 4 year: 2010 ident: 9886_CR47 publication-title: SIAM J. Optim. doi: 10.1137/080744554 – ident: 9886_CR54 – ident: 9886_CR27 doi: 10.1007/s10107-015-0966-2 – volume: 11–12 start-page: 671 year: 1999 ident: 9886_CR59 publication-title: Optim. Methods Softw. doi: 10.1080/10556789908805768 – volume: 23 start-page: 1371 issue: 3 year: 2013 ident: 9886_CR69 publication-title: SIAM J. Optim. doi: 10.1137/110845094 – volume: 32 start-page: 580 issue: 2 year: 2012 ident: 9886_CR48 publication-title: IMA J. Numer. Anal. doi: 10.1093/imanum/drq043 – volume: 63 start-page: 129 issue: 2 year: 1994 ident: 9886_CR11 publication-title: Math. Program. doi: 10.1007/BF01582063 – volume: 30 start-page: 1706 issue: 4 year: 2008 ident: 9886_CR29 publication-title: SIAM J. Sci. Comput. doi: 10.1137/060669930 – start-page: 149 volume-title: System Modelling and Optimization. Methods, Theory and Applications year: 2000 ident: 9886_CR41 doi: 10.1007/978-0-387-35514-6_7 – volume: 1 start-page: 93 issue: 1 year: 1991 ident: 9886_CR62 publication-title: SIAM J. Optim. doi: 10.1137/0801008 – volume: 4 start-page: 1 year: 1995 ident: 9886_CR9 publication-title: Acta Numer. doi: 10.1017/S0962492900002518 – volume: 3 start-page: 751 issue: 4 year: 1993 ident: 9886_CR77 publication-title: SIAM J. Optim. doi: 10.1137/0803039 – volume: 82 start-page: 519 year: 1994 ident: 9886_CR5 publication-title: J. Optim. Theory Appl. doi: 10.1007/BF02192216 – volume-title: Computer Solution of Large Sparse Positive Definite Systems year: 1981 ident: 9886_CR31 – volume: 13 start-page: 241 issue: 3 year: 1977 ident: 9886_CR7 publication-title: Math. Program. doi: 10.1007/BF01584341 – volume: 14 start-page: 1 year: 2005 ident: 9886_CR4 publication-title: Acta Numer. doi: 10.1017/S0962492904000212
SSID	ssj0009732
Score	2.1424654
Snippet	The details of a solver for minimizing a strictly convex quadratic objective function subject to general linear constraints are presented. The method uses a...
SourceID	proquest crossref springer
SourceType	Aggregation Database Enrichment Source Index Database Publisher
StartPage	1
SubjectTerms	Acceleration Algorithms Computation Computer science Convex and Discrete Geometry Lagrange multiplier Linear algebra Management Science Mathematical analysis Mathematical models Mathematics Mathematics and Statistics Methods Operations Research Operations Research/Decision Theory Optimization Projection Quadratic programming Software packages Statistics Studies
SummonAdditionalLinks	– databaseName: Science Database dbid: M2P link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LS8QwEB58HfTg-sT1RQRPSrBpY5qcRETxonhQ8FaaNBFh2dVtV_Tfm8mmuyroxWPbNAmZmcyQ-TIfwCGX6OWqkjrFU8qFtlQnWvtHpZxMKpbpKpBN5Le38vFR3cUDtzrCKts9MWzU1cDgGfkJ1g0TEqupnL28UmSNwuxqpNCYhXkf2TCEdN2kd9Oiu3kgKEtUKqh37Fmb1RxfnTtFsBATVEkpKPvul6bB5o_8aHA7V53_TngFlmPASc7HGrIKM7a_Bp2WzIFE216DpS-VCdfh_pzgJS3yNAyQsIbGExsvRTImnSY-2iU9xJHT2svZEiQAMU3vgwQg-zt5HZUVqpchkbSm3oCHq8v7i2saCRio8dNuqHaJEVbnpiwTl1rObJ5xV1Z-j5ClywXPnQ43ZbXiWkjBxGnmbdxI4Zhh3GabMNcf9O0WEOd8oGB0qa31SuGkYsZJgXRY_iVPbReSdvkLE6uTI0lGr5jWVUaJFYhIQ4kVrAtHk19exqU5_mq820qpiFZaF1MRdeFg8tnbFyZNyr4djLCNyhTmj30Xx60ufOnitwG3_x5wBxZTDBACdHIX5prhyO7BgnlrnuvhflDjT6t--Ns priority: 102 providerName: ProQuest
Title	A dual gradient-projection method for large-scale strictly convex quadratic problems
URI	https://link.springer.com/article/10.1007/s10589-016-9886-1 https://www.proquest.com/docview/1880680349 https://www.proquest.com/docview/1893903041
Volume	67
WOSCitedRecordID	wos000398939500001&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: 1573-2894 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0009732 issn: 0926-6003 databaseCode: 7WY dateStart: 19990101 isFulltext: true titleUrlDefault: https://www.proquest.com/abicomplete providerName: ProQuest – providerCode: PRVPQU databaseName: ABI/INFORM Global customDbUrl: eissn: 1573-2894 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0009732 issn: 0926-6003 databaseCode: M0C dateStart: 19990101 isFulltext: true titleUrlDefault: https://search.proquest.com/abiglobal providerName: ProQuest – providerCode: PRVPQU databaseName: Advanced Technologies & Aerospace Database customDbUrl: eissn: 1573-2894 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0009732 issn: 0926-6003 databaseCode: P5Z dateStart: 19990101 isFulltext: true titleUrlDefault: https://search.proquest.com/hightechjournals providerName: ProQuest – providerCode: PRVPQU databaseName: Computer Science Database customDbUrl: eissn: 1573-2894 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0009732 issn: 0926-6003 databaseCode: K7- dateStart: 19990101 isFulltext: true titleUrlDefault: http://search.proquest.com/compscijour providerName: ProQuest – providerCode: PRVPQU databaseName: Engineering Database customDbUrl: eissn: 1573-2894 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0009732 issn: 0926-6003 databaseCode: M7S dateStart: 19990101 isFulltext: true titleUrlDefault: http://search.proquest.com providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 1573-2894 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0009732 issn: 0926-6003 databaseCode: BENPR dateStart: 19990101 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVPQU databaseName: Science Database customDbUrl: eissn: 1573-2894 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0009732 issn: 0926-6003 databaseCode: M2P dateStart: 19990101 isFulltext: true titleUrlDefault: https://search.proquest.com/sciencejournals providerName: ProQuest – providerCode: PRVAVX databaseName: Springer Journals customDbUrl: eissn: 1573-2894 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0009732 issn: 0926-6003 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/eLvHCXMwnV3dT9swED_xsQd42BgwrRurPGlPTJby4frjkSEQ0kRVAQPGSxQ7Ni9V2ZoWwX-_OzdpC9ombS-WnDhO5DvnLrm73w_gk9Bk5aqSByMyLqT13CbWYteYoJMqzW0VySZUv6-vr82gqeOu22z3NiQZ39RLxW49Su9JJTdaS46fPOto7TTxNZydXy6QdlVkJUtMJjla87wNZf5uiqfGaOFhPguKRltz_Oq_nnILXjauJTuY6cJrWPGjbdhcAhzE3ukcpbXehg3yNGdAzTtwccCoLIvdjmMS2IQ3_2hQbmxGM83Qv2VDyhznNUrWM6L8cJPhI4up6w_s57SsSKEca2hq6l34dnx0cXjCG8oF7nJhJtyGxElvlSvLJGRepF7lIpQVvhV0GZQUKthYG2uNsFLLVPZy3NVOy5C6VPj8DayN7kb-LbAQ0DVwtrTeoxoEbVIXtCQCLDwoMt-BpF37wjV45ESLMSwWSMq0lgXloNFaFmkH9ueX_JiBcfxt8F4r0KLZl3VB6HNSEyZPBz7OT-OOojBJOfJ3UxpjckMRY5zicyvkpSn-dMN3_zT6PWxk5CHE3Mk9WJuMp_4DvHD3KPdxF1bV1fcurH856g_OsPdVcWxPk0NqswG16hzbQe-mG9X_FyRl-DQ
linkProvider	Springer Nature
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1NT9wwEB1RilQ4QIEiFmhrJHopsogT49gHVKG2CARdcVgkbmns2BXSahc2WT7-FL8Rj5OwFKncOPSYxB9K_DyeeJ7nAWxxiatckVOneEy50JbqSGt_qZSTUcESXQSxibTblefn6nQK7tuzMEirbG1iMNTF0OAe-Q7mDRMSs6l8u7yiqBqF0dVWQqOGxbG9u_G_bOXe0Q8_vl_i-OBn7_shbVQFqPGVK6pdZITVqcnzyMWWM5sm3OWFB77MXSp46nQ4_qkV10IKJnYTD1wjhWOGcZv4dt_AW46ZxZAqGJ9OkvymQRAtUrGg3pFI2ihqfVRvF8lJTFAlpaDs73Vw4tw-i8eGZe5g4X_7QO9hvnGoyX49AxZhyg6WYKEVqyCN7VqCuSeZF5eht0_wEBr5MwqUt4o2O1IepaQW1Sbemyd95MnT0uPYEhQ4MVX_jgSi_i25GucFTh9DGlGe8gOcvcqbrsD0YDiwq0Cc846Q0bm21oPeScWMkwLlvvxNHtsORO1wZ6bJvo4iIP1skjcaEZIh4w4RkrEOfH2sclmnHnmp8EaLiqyxQmU2gUQHNh8fe_uBQaF8YIdjLKMShfFx38R2i70nTfyrw7WXO_wM7w57v06yk6Pu8TrMxugMBZroBkxXo7H9CDPmurooR5_CFCLw-7Uh-QByklVm
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Nb9QwEB2VglA5UCitWChgJLiArMaJ17EPCFWUFVXRag9FqriE2LER0mq33WSB_jV-HTNO0i1I9NYDx3zZSvxmPM48zwN4ITXNclXJg5Epl8p6bhNr8dCYoJNKZLaKYhP5eKxPTsxkDX71e2GIVtn7xOioq7mjf-R7VDdMaaqmshc6WsTkYPT29IyTghRlWns5jRYiR_78By7f6jeHBzjWL9N09P743QfeKQxwhw013IbEKW9zV5ZJSL0UPs9kKCs0Al2GXMk82LgV1BpplVZCDTMEsdMqCCekz7DdG3AzxzUm0Qknw8-rgr95FEdLTKo4BhVZn1Ftt-0NiagkFDdaKy7-nBNXge5fudk45Y02_-ePdQ_udoE2228t4z6s-dkWbPYiFqzzaVtw51JFxgdwvM9ocxr7uohUuIZ3f6oQvawV22YY5bMp8ed5jfj2jIRPXDM9Z5HA_5OdLcuKzMqxTqyn3oZP1_KmO7A-m8_8Q2AhYIDkbGm9R2MI2ggXtCIZMDwpUz-ApB_6wnVV2UkcZFqs6kkTWgpi4hFaCjGAVxePnLYlSa66ebdHSNF5p7pYwWMAzy8uo1-hZFE58_Ml3WMyQ3lzbOJ1j8NLTfyrw0dXd_gMbiMSi4-H46PHsJFSjBTZo7uw3iyW_gncct-bb_XiabQmBl-uG5G_AXR3XlI
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+dual+gradient-projection+method+for+large-scale+strictly+convex+quadratic+problems&rft.jtitle=Computational+optimization+and+applications&rft.au=Gould%2C+Nicholas+I.+M.&rft.au=Robinson%2C+Daniel+P.&rft.date=2017-05-01&rft.issn=0926-6003&rft.eissn=1573-2894&rft.volume=67&rft.issue=1&rft.spage=1&rft.epage=38&rft_id=info:doi/10.1007%2Fs10589-016-9886-1&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s10589_016_9886_1
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0926-6003&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0926-6003&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0926-6003&client=summon