Exact semidefinite formulations for a class of (random and non-random) nonconvex quadratic programs

We study a class of quadratically constrained quadratic programs (QCQPs), called diagonal QCQPs , which contain no off-diagonal terms x j x k for j ≠ k , and we provide a sufficient condition on the problem data guaranteeing that the basic Shor semidefinite relaxation is exact. Our condition complem...

Celý popis

Uložené v:

Podrobná bibliografia
Vydané v:	Mathematical programming Ročník 181; číslo 1; s. 1 - 17
Hlavní autori:	Burer, Samuel, Ye, Yinyu
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2020 Springer Nature B.V
Predmet:	Approximation Calculus of Variations and Optimal Control; Optimization Combinatorics Constraints Formulations Full Length Paper Mathematical and Computational Physics Mathematical Methods in Physics Mathematical programming Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Optimization Polynomials Theoretical Variables 90C20 Low-rank solutions 90C26 Semidefinite relaxation Quadratically constrained quadratic programming 90C22
ISSN:	0025-5610, 1436-4646
On-line prístup:	Získať plný text
Tagy:	Pridať tag Žiadne tagy, Buďte prvý, kto otaguje tento záznam!

Abstract	We study a class of quadratically constrained quadratic programs (QCQPs), called diagonal QCQPs , which contain no off-diagonal terms x j x k for j ≠ k , and we provide a sufficient condition on the problem data guaranteeing that the basic Shor semidefinite relaxation is exact. Our condition complements and refines those already present in the literature and can be checked in polynomial time. We then extend our analysis from diagonal QCQPs to general QCQPs, i.e., ones with no particular structure. By reformulating a general QCQP into diagonal form, we establish new, polynomial-time-checkable sufficient conditions for the semidefinite relaxations of general QCQPs to be exact. Finally, these ideas are extended to show that a class of random general QCQPs has exact semidefinite relaxations with high probability as long as the number of constraints grows no faster than a fixed polynomial in the number of variables. To the best of our knowledge, this is the first result establishing the exactness of the semidefinite relaxation for random general QCQPs.
AbstractList	We study a class of quadratically constrained quadratic programs (QCQPs), called diagonal QCQPs, which contain no off-diagonal terms xjxk for j≠k, and we provide a sufficient condition on the problem data guaranteeing that the basic Shor semidefinite relaxation is exact. Our condition complements and refines those already present in the literature and can be checked in polynomial time. We then extend our analysis from diagonal QCQPs to general QCQPs, i.e., ones with no particular structure. By reformulating a general QCQP into diagonal form, we establish new, polynomial-time-checkable sufficient conditions for the semidefinite relaxations of general QCQPs to be exact. Finally, these ideas are extended to show that a class of random general QCQPs has exact semidefinite relaxations with high probability as long as the number of constraints grows no faster than a fixed polynomial in the number of variables. To the best of our knowledge, this is the first result establishing the exactness of the semidefinite relaxation for random general QCQPs. We study a class of quadratically constrained quadratic programs (QCQPs), called diagonal QCQPs , which contain no off-diagonal terms x j x k for j ≠ k , and we provide a sufficient condition on the problem data guaranteeing that the basic Shor semidefinite relaxation is exact. Our condition complements and refines those already present in the literature and can be checked in polynomial time. We then extend our analysis from diagonal QCQPs to general QCQPs, i.e., ones with no particular structure. By reformulating a general QCQP into diagonal form, we establish new, polynomial-time-checkable sufficient conditions for the semidefinite relaxations of general QCQPs to be exact. Finally, these ideas are extended to show that a class of random general QCQPs has exact semidefinite relaxations with high probability as long as the number of constraints grows no faster than a fixed polynomial in the number of variables. To the best of our knowledge, this is the first result establishing the exactness of the semidefinite relaxation for random general QCQPs.
Author	Ye, Yinyu Burer, Samuel
Author_xml	– sequence: 1 givenname: Samuel orcidid: 0000-0001-5886-458X surname: Burer fullname: Burer, Samuel email: samuel-burer@uiowa.edu organization: Department of Management Sciences, University of Iowa – sequence: 2 givenname: Yinyu surname: Ye fullname: Ye, Yinyu organization: Department of Management Science and Engineering, Institute of Computational and Mathematical Engineering, Stanford University
BookMark	eNp9kEtLAzEUhYNUsK3-AVcBN7qIJpNMMrOUUh9QcKPrEPMoU2aSNpmR-u9NO4Lgooubmwvn5Nx8MzDxwVsArgm-JxiLh0QwwQJhUueiXKDiDEwJoxwxzvgETDEuSlRygi_ALKUNxllWVVOgl3ule5hs1xjrGt_0FroQu6FVfRN8OgxQQd2qlGBw8DYqb0IH8wnzDmgc7w53HfyX3cPdoEzMZg23Mayj6tIlOHeqTfbqt8_Bx9PyffGCVm_Pr4vHFdKM0B4xy63iRpdlwQ2vTKENFzXFdWmZYpxQzJnBXIvPuqqFc4TqQjBNCeNYOEbpHNyM7-bg3WBTLzdhiD5HyoLWdZ2_LE6riCgFYYRXWVWMKh1DStE6uY1Np-K3JFgekMsRuczI5RF5zpiD6p9JN_2RYx9V05620tGaco5f2_i31QnXD7mJloE
CitedBy_id	crossref_primary_10_1016_j_ejco_2021_100012 crossref_primary_10_1007_s10957_022_02018_x crossref_primary_10_1007_s10107_023_01985_x crossref_primary_10_1137_21M1399956 crossref_primary_10_1007_s00186_024_00885_w crossref_primary_10_1007_s10107_020_01589_9 crossref_primary_10_1007_s10107_024_02120_0 crossref_primary_10_1080_02331934_2022_2092478 crossref_primary_10_1007_s10107_019_01456_2 crossref_primary_10_1007_s10957_024_02558_4 crossref_primary_10_1007_s10898_022_01268_3 crossref_primary_10_1007_s10957_021_01825_y crossref_primary_10_1109_TCYB_2025_3531105 crossref_primary_10_1007_s10898_025_01478_5 crossref_primary_10_1007_s10107_021_01684_5 crossref_primary_10_1287_moor_2022_1290 crossref_primary_10_1016_j_orl_2024_107108 crossref_primary_10_1007_s10898_025_01497_2 crossref_primary_10_1007_s10898_025_01499_0 crossref_primary_10_1016_j_jsc_2023_102258 crossref_primary_10_3390_math8020153 crossref_primary_10_1007_s10898_020_00918_8 crossref_primary_10_1287_moor_2022_1305 crossref_primary_10_1007_s10107_022_01912_6 crossref_primary_10_1007_s10898_021_01071_6 crossref_primary_10_1137_22M1528215 crossref_primary_10_1137_21M140345X crossref_primary_10_1007_s10107_024_02073_4 crossref_primary_10_1007_s10107_024_02076_1 crossref_primary_10_1137_22M1507656 crossref_primary_10_1007_s10898_022_01255_8 crossref_primary_10_1007_s10898_022_01258_5 crossref_primary_10_1007_s10898_024_01407_y crossref_primary_10_1007_s10107_024_02105_z
Cites_doi	10.1137/S105262340139001X 10.1137/110826862 10.1007/BF02591902 10.1007/s10107-017-1157-0 10.1287/moor.19.1.38 10.1007/BF02574037 10.1023/A:1008282830093 10.1137/14099379X 10.1287/moor.23.2.339 10.1109/MSP.2010.936019 10.1007/978-3-642-61578-8 10.1007/s10107-015-0888-z 10.1002/cpa.21432 10.1287/moor.24.1.176 10.1137/070697835 10.1145/4221.4222 10.1145/990308.990310 10.1007/PL00011420 10.1007/BF01580646 10.1287/moor.28.2.246.14485 10.1007/s10107980012a 10.1007/978-3-642-04295-9 10.1017/S0962492901000071 10.1007/s10107-002-0352-8 10.1007/s10107-016-1059-6 10.1007/s10107-013-0648-x 10.1007/s10898-017-0521-1 10.1137/130915261 10.1137/1.9781611973075.57 10.1007/978-3-319-00200-2_16
ContentType	Journal Article
Copyright	Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2019 Mathematical Programming is a copyright of Springer, (2019). All Rights Reserved. Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2019.
Copyright_xml	– notice: Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2019 – notice: Mathematical Programming is a copyright of Springer, (2019). All Rights Reserved. – notice: Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2019.
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/s10107-019-01367-2
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 ProQuest Advanced Technologies & Aerospace 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 (New) 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 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 url: https://www.proquest.com/central sourceTypes: Aggregation Database
DeliveryMethod	fulltext_linktorsrc
Discipline	Engineering Mathematics
EISSN	1436-4646
EndPage	17
ExternalDocumentID	10_1007_s10107_019_01367_2
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.- L7M L~C L~D PKEHL PQEST PQUKI PRINS Q9U
ID	FETCH-LOGICAL-c413t-4e6ea6dc5526d68d2cd6793095e4a4613064d06c7b9897ff13c274c314607f433
IEDL.DBID	RSV
ISICitedReferencesCount	40
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000531046500001&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 Sep 25 00:44:46 EDT 2025 Thu Sep 25 00:41:52 EDT 2025 Sat Nov 29 03:34:01 EST 2025 Tue Nov 18 22:05:39 EST 2025 Fri Feb 21 02:48:21 EST 2025
IsPeerReviewed	true
IsScholarly	true
Issue	1
Keywords	90C20 Low-rank solutions 90C26 Semidefinite relaxation Quadratically constrained quadratic programming 90C22
Language	English
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c413t-4e6ea6dc5526d68d2cd6793095e4a4613064d06c7b9897ff13c274c314607f433
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ORCID	0000-0001-5886-458X
PQID	2175714168
PQPubID	25307
PageCount	17
ParticipantIDs	proquest_journals_2399901373 proquest_journals_2175714168 crossref_primary_10_1007_s10107_019_01367_2 crossref_citationtrail_10_1007_s10107_019_01367_2 springer_journals_10_1007_s10107_019_01367_2
PublicationCentury	2000
PublicationDate	2020-05-01
PublicationDateYYYYMMDD	2020-05-01
PublicationDate_xml	– month: 05 year: 2020 text: 2020-05-01 day: 01
PublicationDecade	2020
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	2020
Publisher	Springer Berlin Heidelberg Springer Nature B.V
Publisher_xml	– name: Springer Berlin Heidelberg – name: Springer Nature B.V
References	Todd (CR31) 1986; 35 Sturm, Zhang (CR29) 2003; 28 Bandeira, Boumal, Singer (CR4) 2017; 163 Smale (CR25) 1983; 27 Fujie, Kojima (CR16) 1997; 10 Todd, Tunçel, Ye (CR32) 2001; 90 Deza, Laurent (CR14) 1997 Ye (CR34) 1994; 19 Barvinok (CR5) 1995; 13 Burer, Anstreicher (CR11) 2013; 23 Beck, Pan (CR6) 2017; 69 Ye (CR35) 1999; 81 Burer (CR10) 2015; 151 Sojoudi, Lavaei (CR27) 2014; 24 Pataki (CR21) 1998; 23 Candès, Strohmer, Voroninski (CR13) 2013; 66 Recht, Fazel, Parrilo (CR22) 2010; 52 Spielman, Teng (CR28) 2004; 51 Anjos, Lasserre (CR2) 2012 Todd (CR30) 2001; 10 CR8 Madani, Sojoudi, Fazelnia, Lavaei (CR20) 2017; 27 CR7 CR26 CR24 CR23 Laurent, Varvitsiotis (CR17) 2014; 145 Borgwardt (CR9) 1987 Ye, Zhang (CR36) 2003; 14 Madani, Fazelnia, Lavaei (CR19) 2014 Burer, Monteiro (CR12) 2003; 95 Adler, Megiddo (CR1) 1985; 32 Luo, Ma, So, Ye, Zhang (CR18) 2010; 27 Anstreicher, Ji, Potra, Ye (CR3) 1999; 24 Diestel (CR15) 2018 Yang, Anstreicher, Burer (CR33) 2018; 170 M Laurent (1367_CR17) 2014; 145 R Madani (1367_CR20) 2017; 27 S Smale (1367_CR25) 1983; 27 MJ Todd (1367_CR31) 1986; 35 S Burer (1367_CR12) 2003; 95 Y Ye (1367_CR34) 1994; 19 AS Bandeira (1367_CR4) 2017; 163 S Burer (1367_CR11) 2013; 23 I Adler (1367_CR1) 1985; 32 Y Ye (1367_CR35) 1999; 81 B Recht (1367_CR22) 2010; 52 A Barvinok (1367_CR5) 1995; 13 S Burer (1367_CR10) 2015; 151 KM Anstreicher (1367_CR3) 1999; 24 1367_CR7 B Yang (1367_CR33) 2018; 170 1367_CR8 R Diestel (1367_CR15) 2018 M Todd (1367_CR30) 2001; 10 MJ Todd (1367_CR32) 2001; 90 DA Spielman (1367_CR28) 2004; 51 G Pataki (1367_CR21) 1998; 23 (1367_CR2) 2012 KH Borgwardt (1367_CR9) 1987 T Fujie (1367_CR16) 1997; 10 S Sojoudi (1367_CR27) 2014; 24 Y Ye (1367_CR36) 2003; 14 A Beck (1367_CR6) 2017; 69 EJ Candès (1367_CR13) 2013; 66 JF Sturm (1367_CR29) 2003; 28 1367_CR26 1367_CR23 1367_CR24 MM Deza (1367_CR14) 1997 R Madani (1367_CR19) 2014 ZQ Luo (1367_CR18) 2010; 27
References_xml	– volume: 14 start-page: 245 issue: 1 year: 2003 end-page: 267 ident: CR36 article-title: New results on quadratic minimization publication-title: SIAM J. Optim. doi: 10.1137/S105262340139001X – volume: 23 start-page: 432 issue: 1 year: 2013 end-page: 451 ident: CR11 article-title: Second-order-cone constraints for extended trust-region subproblems publication-title: SIAM J. Optim. doi: 10.1137/110826862 – volume: 27 start-page: 241 issue: 3 year: 1983 end-page: 262 ident: CR25 article-title: On the average number of steps of the simplex method of linear programming publication-title: Math. Program. doi: 10.1007/BF02591902 – volume: 170 start-page: 541 issue: 2 year: 2018 end-page: 553 ident: CR33 article-title: Quadratic programs with hollows publication-title: Math. Program. doi: 10.1007/s10107-017-1157-0 – volume: 19 start-page: 38 issue: 1 year: 1994 end-page: 52 ident: CR34 article-title: Toward probabilistic analysis of interior-point algorithms for linear programming publication-title: Math. Oper. Res. doi: 10.1287/moor.19.1.38 – year: 2012 ident: CR2 publication-title: Handbook on Semidefinite, Conic and Polynomial Optimization – volume: 13 start-page: 189 year: 1995 end-page: 202 ident: CR5 article-title: Problems of distance geometry and convex properties of quadratic maps publication-title: Discrete Comput. Geom. doi: 10.1007/BF02574037 – volume: 10 start-page: 367 issue: 4 year: 1997 end-page: 380 ident: CR16 article-title: Semidefinite programming relaxation for nonconvex quadratic programs publication-title: J. Global Optim. doi: 10.1023/A:1008282830093 – volume: 27 start-page: 725 issue: 2 year: 2017 end-page: 758 ident: CR20 article-title: Finding low-rank solutions of sparse linear matrix inequalities using convex optimization publication-title: SIAM J. Optim. doi: 10.1137/14099379X – volume: 23 start-page: 339 year: 1998 end-page: 358 ident: CR21 article-title: On the rank of extreme matrices in semidefinite programs and the multiplicity of optimal eigenvalues publication-title: Math. Oper. Res. doi: 10.1287/moor.23.2.339 – volume: 27 start-page: 20 issue: 3 year: 2010 end-page: 34 ident: CR18 article-title: Semidefinite relaxation of quadratic optimization problems publication-title: IEEE Signal Process. Mag. doi: 10.1109/MSP.2010.936019 – year: 1987 ident: CR9 publication-title: The Simplex Method—A Probabilistic Approach doi: 10.1007/978-3-642-61578-8 – ident: CR8 – year: 2018 ident: CR15 publication-title: Graph Theory, Volume 173 of Graduate Texts in Mathematics – year: 2014 ident: CR19 publication-title: Rank-2 Matrix Solution for Semidefinite Relaxations of Arbitrary Polynomial Optimization Problems – volume: 151 start-page: 89 issue: 1, Ser. B year: 2015 end-page: 116 ident: CR10 article-title: A gentle, geometric introduction to copositive optimization publication-title: Math. Program. doi: 10.1007/s10107-015-0888-z – ident: CR23 – volume: 66 start-page: 1241 issue: 8 year: 2013 end-page: 1274 ident: CR13 article-title: PhaseLift: exact and stable signal recovery from magnitude measurements via convex programming publication-title: Commun. Pure Appl. Math. doi: 10.1002/cpa.21432 – volume: 24 start-page: 176 issue: 1 year: 1999 end-page: 192 ident: CR3 article-title: Probabilistic analysis of an infeasible-interior-point algorithm for linear programming publication-title: Math. Oper. Res. doi: 10.1287/moor.24.1.176 – volume: 52 start-page: 471 issue: 3 year: 2010 end-page: 501 ident: CR22 article-title: Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization publication-title: SIAM Rev. doi: 10.1137/070697835 – volume: 32 start-page: 871 issue: 4 year: 1985 end-page: 895 ident: CR1 article-title: A simplex algorithm whose average number of steps is bounded between two quadratic functions of the smaller dimension publication-title: J. Assoc. Comput. Mach. doi: 10.1145/4221.4222 – volume: 51 start-page: 385 issue: 3 year: 2004 end-page: 463 ident: CR28 article-title: Smoothed analysis of algorithms: why the simplex algorithm usually takes polynomial time publication-title: J. ACM doi: 10.1145/990308.990310 – volume: 90 start-page: 59 issue: 1, Ser. A year: 2001 end-page: 69 ident: CR32 article-title: Characterizations, bounds, and probabilistic analysis of two complexity measures for linear programming problems publication-title: Math. Program. doi: 10.1007/PL00011420 – volume: 35 start-page: 173 issue: 2 year: 1986 end-page: 192 ident: CR31 article-title: Polynomial expected behavior of a pivoting algorithm for linear complementarity and linear programming problems publication-title: Math. Program. doi: 10.1007/BF01580646 – volume: 28 start-page: 246 issue: 2 year: 2003 end-page: 267 ident: CR29 article-title: On cones of nonnegative quadratic functions publication-title: Math. Oper. Res. doi: 10.1287/moor.28.2.246.14485 – volume: 81 start-page: 219 issue: 2 year: 1999 end-page: 226 ident: CR35 article-title: Approximating quadratic programming with bound and quadratic constraints publication-title: Math. Program. doi: 10.1007/s10107980012a – year: 1997 ident: CR14 publication-title: Geometry of Cuts and Metrics. Algorithms and Combinatorics doi: 10.1007/978-3-642-04295-9 – volume: 10 start-page: 515 year: 2001 end-page: 560 ident: CR30 article-title: Semidefinite optimization publication-title: Acta Numer. doi: 10.1017/S0962492901000071 – volume: 95 start-page: 329 issue: 2, Ser. B year: 2003 end-page: 357 ident: CR12 article-title: A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization publication-title: Math. Program. doi: 10.1007/s10107-002-0352-8 – ident: CR7 – volume: 163 start-page: 145 issue: 1–2, Ser. A year: 2017 end-page: 167 ident: CR4 article-title: Tightness of the maximum likelihood semidefinite relaxation for angular synchronization publication-title: Math. Program. doi: 10.1007/s10107-016-1059-6 – volume: 145 start-page: 291 issue: 1–2, Ser. A year: 2014 end-page: 325 ident: CR17 article-title: A new graph parameter related to bounded rank positive semidefinite matrix completions publication-title: Math. Program. doi: 10.1007/s10107-013-0648-x – ident: CR26 – volume: 69 start-page: 309 issue: 2 year: 2017 end-page: 342 ident: CR6 article-title: A branch and bound algorithm for nonconvex quadratic optimization with ball and linear constraints publication-title: J. Global Optim. doi: 10.1007/s10898-017-0521-1 – ident: CR24 – volume: 24 start-page: 1746 issue: 4 year: 2014 end-page: 1778 ident: CR27 article-title: Exactness of semidefinite relaxations for nonlinear optimization problems with underlying graph structure publication-title: SIAM J. Optim. doi: 10.1137/130915261 – volume: 95 start-page: 329 issue: 2, Ser. B year: 2003 ident: 1367_CR12 publication-title: Math. Program. doi: 10.1007/s10107-002-0352-8 – ident: 1367_CR7 – volume: 32 start-page: 871 issue: 4 year: 1985 ident: 1367_CR1 publication-title: J. Assoc. Comput. Mach. doi: 10.1145/4221.4222 – volume-title: Rank-2 Matrix Solution for Semidefinite Relaxations of Arbitrary Polynomial Optimization Problems year: 2014 ident: 1367_CR19 – volume: 145 start-page: 291 issue: 1–2, Ser. A year: 2014 ident: 1367_CR17 publication-title: Math. Program. doi: 10.1007/s10107-013-0648-x – volume: 14 start-page: 245 issue: 1 year: 2003 ident: 1367_CR36 publication-title: SIAM J. Optim. doi: 10.1137/S105262340139001X – volume: 24 start-page: 176 issue: 1 year: 1999 ident: 1367_CR3 publication-title: Math. Oper. Res. doi: 10.1287/moor.24.1.176 – volume: 28 start-page: 246 issue: 2 year: 2003 ident: 1367_CR29 publication-title: Math. Oper. Res. doi: 10.1287/moor.28.2.246.14485 – volume: 151 start-page: 89 issue: 1, Ser. B year: 2015 ident: 1367_CR10 publication-title: Math. Program. doi: 10.1007/s10107-015-0888-z – volume: 90 start-page: 59 issue: 1, Ser. A year: 2001 ident: 1367_CR32 publication-title: Math. Program. doi: 10.1007/PL00011420 – ident: 1367_CR24 – volume: 163 start-page: 145 issue: 1–2, Ser. A year: 2017 ident: 1367_CR4 publication-title: Math. Program. doi: 10.1007/s10107-016-1059-6 – volume: 69 start-page: 309 issue: 2 year: 2017 ident: 1367_CR6 publication-title: J. Global Optim. doi: 10.1007/s10898-017-0521-1 – volume: 35 start-page: 173 issue: 2 year: 1986 ident: 1367_CR31 publication-title: Math. Program. doi: 10.1007/BF01580646 – volume: 13 start-page: 189 year: 1995 ident: 1367_CR5 publication-title: Discrete Comput. Geom. doi: 10.1007/BF02574037 – volume-title: Graph Theory, Volume 173 of Graduate Texts in Mathematics year: 2018 ident: 1367_CR15 – ident: 1367_CR8 – volume: 81 start-page: 219 issue: 2 year: 1999 ident: 1367_CR35 publication-title: Math. Program. doi: 10.1007/s10107980012a – volume: 10 start-page: 515 year: 2001 ident: 1367_CR30 publication-title: Acta Numer. doi: 10.1017/S0962492901000071 – volume: 10 start-page: 367 issue: 4 year: 1997 ident: 1367_CR16 publication-title: J. Global Optim. doi: 10.1023/A:1008282830093 – volume: 23 start-page: 432 issue: 1 year: 2013 ident: 1367_CR11 publication-title: SIAM J. Optim. doi: 10.1137/110826862 – volume: 27 start-page: 725 issue: 2 year: 2017 ident: 1367_CR20 publication-title: SIAM J. Optim. doi: 10.1137/14099379X – ident: 1367_CR26 doi: 10.1137/1.9781611973075.57 – volume-title: Handbook on Semidefinite, Conic and Polynomial Optimization year: 2012 ident: 1367_CR2 – volume: 27 start-page: 20 issue: 3 year: 2010 ident: 1367_CR18 publication-title: IEEE Signal Process. Mag. doi: 10.1109/MSP.2010.936019 – volume: 51 start-page: 385 issue: 3 year: 2004 ident: 1367_CR28 publication-title: J. ACM doi: 10.1145/990308.990310 – volume-title: The Simplex Method—A Probabilistic Approach year: 1987 ident: 1367_CR9 doi: 10.1007/978-3-642-61578-8 – volume: 23 start-page: 339 year: 1998 ident: 1367_CR21 publication-title: Math. Oper. Res. doi: 10.1287/moor.23.2.339 – ident: 1367_CR23 doi: 10.1007/978-3-319-00200-2_16 – volume: 66 start-page: 1241 issue: 8 year: 2013 ident: 1367_CR13 publication-title: Commun. Pure Appl. Math. doi: 10.1002/cpa.21432 – volume: 19 start-page: 38 issue: 1 year: 1994 ident: 1367_CR34 publication-title: Math. Oper. Res. doi: 10.1287/moor.19.1.38 – volume: 170 start-page: 541 issue: 2 year: 2018 ident: 1367_CR33 publication-title: Math. Program. doi: 10.1007/s10107-017-1157-0 – volume: 24 start-page: 1746 issue: 4 year: 2014 ident: 1367_CR27 publication-title: SIAM J. Optim. doi: 10.1137/130915261 – volume-title: Geometry of Cuts and Metrics. Algorithms and Combinatorics year: 1997 ident: 1367_CR14 doi: 10.1007/978-3-642-04295-9 – volume: 27 start-page: 241 issue: 3 year: 1983 ident: 1367_CR25 publication-title: Math. Program. doi: 10.1007/BF02591902 – volume: 52 start-page: 471 issue: 3 year: 2010 ident: 1367_CR22 publication-title: SIAM Rev. doi: 10.1137/070697835
SSID	ssj0001388
Score	2.5168612
Snippet	We study a class of quadratically constrained quadratic programs (QCQPs), called diagonal QCQPs , which contain no off-diagonal terms x j x k for j ≠ k , and... We study a class of quadratically constrained quadratic programs (QCQPs), called diagonal QCQPs, which contain no off-diagonal terms xjxk for j≠k, and we...
SourceID	proquest crossref springer
SourceType	Aggregation Database Enrichment Source Index Database Publisher
StartPage	1
SubjectTerms	Approximation Calculus of Variations and Optimal Control; Optimization Combinatorics Constraints Formulations Full Length Paper Mathematical and Computational Physics Mathematical Methods in Physics Mathematical programming Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Optimization Polynomials Theoretical Variables
SummonAdditionalLinks	– databaseName: Science Database dbid: M2P link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LT8MwDI54HeDAGzEYKAcOIIggTZumJ4TQEAdAHADtVnVOIk2CDehA_HzsLt0AwS5cqlpplUqfa39OHJuxvU7mpfGRFYg9iFilVhQ61sIkUNgEZNap-pA9XKU3N6bdzm7DglsZ0iprm1gZatsHWiM_RuqcpBLpgzl9fhHUNYp2V0MLjWk2i8xGUkrXdXQ7ssRSGVO3bCWeEA7NhKNzskq6pGwhhcYi-u6YxmzzxwZp5Xculv77xctsMTBOfjZUkRU25XqrbOFLHUKUrkfFW8s1Bq2PAga8dE9d63yXSCknahsafZUk8IID8W7e93wf3Z3tP3G88l6_J4biAd1XOe0f_OWtsKRpwEM6WLnO7i9ad-eXIvRiEIBubiBip12hLSRJpK02NgKrEV4kaC4uYgpCdGxPNKSdzGSp91IBxrug0BCfpD5WaoPN4LRuk3F0gF45H4O3FsmaQo4HKQZuWhrw0hcNJmsgcgiFyqlfxmM-LrFM4OUIXl6Bl0cNdjh653lYpmPi080asTz8smU-huv3YWRyGdVnVA12VKvEePjvybYmT7bN5iMK4ascyiabGby-uR02B--Dbvm6W-nzJ6FE-Qs priority: 102 providerName: ProQuest
Title	Exact semidefinite formulations for a class of (random and non-random) nonconvex quadratic programs
URI	https://link.springer.com/article/10.1007/s10107-019-01367-2 https://www.proquest.com/docview/2175714168 https://www.proquest.com/docview/2399901373
Volume	181
WOSCitedRecordID	wos000531046500001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVAVX databaseName: SpringerLINK Contemporary 1997-Present customDbUrl: eissn: 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/eLvHCXMwnV3dT9swED8x4GF7AAZDlI_KDzwMbZbqOLGdR0BFSEBV8TXGS5SebakStBspE38-5zRpAQHSeDnFshNHd_bd7-TzHcB2L_XC-Mhykj3yWGrLcxUrbhLMbYIi7ZV1yC6Pdadjrq7SbnUprKij3esjyVJTP7nsJsowyRDfI2l7k-KdI3NnQsGG07PLif4V0pi6UGtAB9VVmde_8dwcTTHmi2PR0tocLH7sP5dgoUKXbHe8HL7CjBssw5cnOQepdTJJ1FqsALYfchyxwt32rfP9AEBZgLFVUa8iNFjOMGBsNvTsO5k2O7xlRNlgOODj5k54LuPXH9jf-9yGVYWsCv0qvsHFQft8_5BXdRc4kkkb8dgplyuLSRIpq4yN0CoSJYExF-dxcDhUbFsKdS81qfZeSCTfFiUp3Zb2sZSrMEvTujVgZOy8dD5Gby0BM0l4DjU5aUoY9MLnDRA1-zOskpKH2hg32TSdcmBnRuzMSnZmUQN-TN75M07J8e7ozVqqWbU9i4z8sEQLwqLm9W5CbWnIxSgb8LMW8rT77cnW_2_4BnyOgvtexk9uwuzo7t5twTz-G_WLuyZ80r9-N2Fur93pnlLrSHOiJ639QKNuoPqMaDe5bpY74BGD7fY0
linkProvider	Springer Nature
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Nb9QwEB1VpRJwoOVLXVrAB5BAYFE7juMcKlRBq1bdrnooqLeQHdvSSu1u22y__hS_kZlsslsQ9NYDlyhWEjmJn5_f2OMZgDf9PCoXtZfU9ihNknlZWmOlS7H0Kaq8X-ch-97Nej13eJjvz8HPdi8Mu1W2nFgTtR8hz5F_IumcZorkg_t8cio5axSvrrYpNCaw2A3Xl2SyVes7X6l932q9tXnwZVs2WQUkEmGPpQk2lNZjmmrrrfMavaUXJakRTGlYTlvj1yxm_dzlWYwqQbLcMCFKWcui4QlQovx7hiOLsaug3p8yv0qca1PEsi5pNuk0W_VU7eTJ3kkJkZP-fSCcqds_FmTrcW5r8X_7Q0vwqFHUYmPSBR7DXBg-gYc34ixSaW8anLZ6Crh5VeJYVOF44EMcsOgWLN2bRGYVF0QpkO0KMYriHQ3nfnQs6CiGo6GcFN_zee2zfyVOz0vPPQlF4-5WPYNvd_LNz2Geqg3LIGiAj0mIBqP3JEYT0rCYkWFqlcOoYtkB1TZ8gU0gds4HclTMQkgzWAoCS1GDpdAd-DB95mQShuTWu1dbhBQNJVXFDB5_v0xKNef4k0kHPrYQnF3-d2Uvbq_sNdzfPtjrFt2d3u4KPNA8XVH7i67C_PjsPLyEBbwYD6qzV3VfEvDjrqH5C5zwUxE
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3dS8MwEA-iIvrgtzidmgcfFC2aJk3TR1GH4hwDP_CtdJcEBrrp2sn-fC9du01RQXwpDUmbkEtyvyO_uyNkvxVZpqyvPZQ9eIKH2kukkJ4KINEBsKiV5yF7rIeNhnp6ipoTXvw52728khz6NLgoTZ3s5FXbkwnHN5ZTJh3Xh-NWx0N4RjgivbPX7x5HZzHjSpVJWx1SKNxmvv_HZ9U0xptfrkhzzVNb-v-Yl8ligTrp2XCZrJAp01klCxOxCLF0Owrgmq4RuBwkkNHUvLS1sW0HTKmDt0Wyr9QVaELBYW_atfQAVZ7uvlB80k634w2Lh-4957UP6Fs_0W61AS0oYek6eahd3p9feUU-Bg9Q1WWeMNIkUkMQ-FJLpX3QEkWMIM2IRDhDRAp9KiFsRSoKrWUc0OYFjofxaWgF5xtkGrs1m4SiErTcWAFWawRsHHEehGi8SabAMptUCCtFEUMRrNzlzHiOx2GW3XTGOJ1xPp2xXyFHo29eh6E6fm1dLSUcF9s2jdE-C0KGGFV9X41oLnIxGnmFHJcCH1f_3NnW35rvkbnmRS2uXzdutsm87yz8nGJZJdNZr292yCy8Z-20t5sv9g-LBfrB
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=Exact+semidefinite+formulations+for+a+class+of+%28random+and+non-random%29+nonconvex+quadratic+programs&rft.jtitle=Mathematical+programming&rft.au=Burer%2C+Samuel&rft.au=Ye%2C+Yinyu&rft.date=2020-05-01&rft.pub=Springer+Berlin+Heidelberg&rft.issn=0025-5610&rft.eissn=1436-4646&rft.volume=181&rft.issue=1&rft.spage=1&rft.epage=17&rft_id=info:doi/10.1007%2Fs10107-019-01367-2&rft.externalDocID=10_1007_s10107_019_01367_2
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