Mixing convex-optimization bounds for maximum-entropy sampling

The maximum-entropy sampling problem is a fundamental and challenging combinatorial-optimization problem, with application in spatial statistics. It asks to find a maximum-determinant order- s principal submatrix of an order- n covariance matrix. Exact solution methods for this NP-hard problem are b...

Full description

Saved in:

Bibliographic Details
Published in	Mathematical programming Vol. 188; no. 2; pp. 539 - 568
Main Authors	Chen, Zhongzhu, Fampa, Marcia, Lambert, Amélie, Lee, Jon
Format	Journal Article
Language	English
Published	Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2021 Springer Nature B.V Springer Verlag
Subjects	Calculus of Variations and Optimal Control; Optimization Combinatorial analysis Combinatorics Convexity Covariance matrix Entropy Exact solutions Full Length Paper Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Optimization Optimization and Control Sampling Theoretical Upper bounds Mixing 90C51 Convex optimization 90C25 Maximum-entropy sampling 90C27 62H11 62K99 maximum-entropy sampling convex optimization Mathematics Subject Classification 90C25
Online Access	Get full text

Cover

Loading…

Abstract	The maximum-entropy sampling problem is a fundamental and challenging combinatorial-optimization problem, with application in spatial statistics. It asks to find a maximum-determinant order- s principal submatrix of an order- n covariance matrix. Exact solution methods for this NP-hard problem are based on a branch-and-bound framework. Many of the known upper bounds for the optimal value are based on convex optimization. We present a methodology for “mixing” these bounds to achieve better bounds.
AbstractList	The maximum-entropy sampling problem is a fundamental and challenging combinatorial-optimization problem, with application in spatial statistics. It asks to find a maximum-determinant order- s principal submatrix of an order- n covariance matrix. Exact solution methods for this NP-hard problem are based on a branch-and-bound framework. Many of the known upper bounds for the optimal value are based on convex optimization. We present a methodology for “mixing” these bounds to achieve better bounds. The maximum-entropy sampling problem is a fundamental and challenging combinatorial-optimization problem, with application in spatial statistics. It asks to find a maximum-determinant order-$s$ principal submatrix of an order-$n$ covariance matrix. Exact solution methods for this NP-hard problem are based on a branch-and-bound framework. Many of the known upper bounds for the optimal value are based on convex optimization. We present a methodology for "mixing" these bounds to achieve better bounds.
Author	Lee, Jon Fampa, Marcia Chen, Zhongzhu Lambert, Amélie
Author_xml	– sequence: 1 givenname: Zhongzhu surname: Chen fullname: Chen, Zhongzhu organization: University of Michigan – sequence: 2 givenname: Marcia surname: Fampa fullname: Fampa, Marcia organization: Universidade Federal do Rio de Janeiro – sequence: 3 givenname: Amélie surname: Lambert fullname: Lambert, Amélie organization: Conservatoire National des Arts et Métiers – sequence: 4 givenname: Jon orcidid: 0000-0002-8190-1091 surname: Lee fullname: Lee, Jon email: jonxlee@umich.edu organization: University of Michigan
BackLink	https://hal.science/hal-03016397$$DView record in HAL
BookMark	eNp9kE1LAzEQhoNUsK3-AU8LnjxEJ8lmN70IpagVKl70HGJ2U1O6yZpsv_z1brui4KGngeF93hmeAeo570qELgncEID8NhIgkGOggIFwIfDmBPVJyjKcZmnWQ30AyjHPCJyhQYwLACBMiD66e7Zb6-aJ9m5dbrGvG1vZL9VY75J3v3JFTIwPSaW2tlpVuHRN8PUuiaqqly13jk6NWsby4mcO0dvD_etkimcvj0-T8QxrNsobzEwxMpSykeEGqEg15IaXoBUIpbSheSGoAhAjnqam4IpmXGvFDTUaiGGCDdF11_uhlrIOtlJhJ72ycjqeyf0OGJCsvbUmbfaqy9bBf67K2MiFXwXXvicp55QKkbO0TdEupYOPMZTmt5aA3DuVnVPZOpUHp3LTQuIfpG1zkNUEZZfHUdahsb3j5mX4--oI9Q06VI3D
CitedBy_id	crossref_primary_10_1287_opre_2022_2324 crossref_primary_10_1007_s43069_020_0011_z crossref_primary_10_1007_s10107_024_02101_3 crossref_primary_10_1287_ijoc_2022_1264 crossref_primary_10_1016_j_dam_2023_04_020 crossref_primary_10_1287_ijoc_2022_0235 crossref_primary_10_1016_j_dam_2024_01_002
Cites_doi	10.1007/978-1-4615-4381-7_17 10.1007/s10898-018-0662-x 10.1007/3-540-61310-2_18 10.1287/opre.46.5.655 10.1017/CBO9780511804441 10.1080/02664768700000020 10.1007/978-1-4614-0769-0_25 10.1016/S0166-218X(00)00217-1 10.23943/princeton/9780691128894.001.0001 10.1007/s10107-005-0661-9 10.1007/978-3-7908-2693-7_1 10.1007/s10107-012-0514-2 10.1287/opre.2019.1962 10.1007/s10107-006-0024-1 10.1287/opre.43.4.684 10.1007/978-3-642-57576-1_16 10.1007/s10107-002-0318-x 10.1017/CBO9780511810817 10.1080/10556789908805762 10.1137/1.9781611971316 10.1287/ijoc.2016.0731 10.1007/s101070050055 10.1007/BF02055196
ContentType	Journal Article
Copyright	Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2021 Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2021. Distributed under a Creative Commons Attribution 4.0 International License
Copyright_xml	– notice: Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2021 – notice: Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2021. – notice: Distributed under a Creative Commons Attribution 4.0 International License
DBID	AAYXX CITATION 7SC 8FD JQ2 L7M L~C L~D 1XC VOOES
DOI	10.1007/s10107-020-01588-w
DatabaseName	CrossRef Computer and Information Systems Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional Hyper Article en Ligne (HAL) Hyper Article en Ligne (HAL) (Open Access)
DatabaseTitle	CrossRef Computer and Information Systems Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Advanced Technologies Database with Aerospace ProQuest Computer Science Collection Computer and Information Systems Abstracts Professional
DatabaseTitleList	Computer and Information Systems Abstracts
DeliveryMethod	fulltext_linktorsrc
Discipline	Engineering Mathematics
EISSN	1436-4646
EndPage	568
ExternalDocumentID	oai_HAL_hal_03016397v1 10_1007_s10107_020_01588_w
GrantInformation_xml	– fundername: Office of Naval Research (US) grantid: N00014-17-1-2296 – fundername: Air Force Office of Scientific Research grantid: FA9550-19-1-0175 funderid: http://dx.doi.org/10.13039/100000181 – fundername: CNPq grantid: 303898/2016-0; 434683/2018-3
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 ACSTC ADHKG ADXHL AEZWR AFDZB AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP AMVHM ATHPR AYFIA CITATION PHGZM PHGZT 7SC 8FD ABRTQ JQ2 L7M L~C L~D 1XC VOOES
ID	FETCH-LOGICAL-c397t-3fd9f2239f5f0284c07f5e0ca08aacf27d82a0089544fd5a265cca5f2fc01f383
IEDL.DBID	U2A
ISSN	0025-5610
IngestDate	Thu Jul 10 08:57:08 EDT 2025 Fri Jul 25 19:39:08 EDT 2025 Thu Apr 24 23:12:17 EDT 2025 Tue Jul 01 02:15:13 EDT 2025 Fri Feb 21 02:48:22 EST 2025
IsDoiOpenAccess	true
IsOpenAccess	true
IsPeerReviewed	true
IsScholarly	true
Issue	2
Keywords	Mixing 90C51 Convex optimization 90C25 Maximum-entropy sampling 90C27 62H11 62K99 maximum-entropy sampling convex optimization Mathematics Subject Classification 90C25
Language	English
License	Distributed under a Creative Commons Attribution 4.0 International License: http://creativecommons.org/licenses/by/4.0
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c397t-3fd9f2239f5f0284c07f5e0ca08aacf27d82a0089544fd5a265cca5f2fc01f383
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ORCID	0000-0002-8190-1091 0000-0001-8305-2145
OpenAccessLink	https://hal.science/hal-03016397
PQID	2552288734
PQPubID	25307
PageCount	30
ParticipantIDs	hal_primary_oai_HAL_hal_03016397v1 proquest_journals_2552288734 crossref_primary_10_1007_s10107_020_01588_w crossref_citationtrail_10_1007_s10107_020_01588_w springer_journals_10_1007_s10107_020_01588_w
ProviderPackageCode	CITATION AAYXX
PublicationCentury	2000
PublicationDate	2021-08-01
PublicationDateYYYYMMDD	2021-08-01
PublicationDate_xml	– month: 08 year: 2021 text: 2021-08-01 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	2021
Publisher	Springer Berlin Heidelberg Springer Nature B.V Springer Verlag
Publisher_xml	– name: Springer Berlin Heidelberg – name: Springer Nature B.V – name: Springer Verlag
References	BakonyiMWoerdemanHJMatrix Completions, Moments, and Sums of Hermitian Squares2011PrincetonPrinceton University Press10.23943/princeton/9780691128894.001.0001 Löfberg, J.: Yalmip: A toolbox for modeling and optimization in Matlab. In: Proceedings of the CACSD Conference (2004) Fedorov, V., Lee, J.: Design of experiments in statistics. In: Handbook of Semidefinite Programming, volume 27 of Internat. Ser. Oper. Res. Management Sci., pp. 511–532. Kluwer Acad. Publ., Boston, MA (2000) ZhangFThe Schur Complement and its Applications. Numerical Methods and Algorithms2005New YorkSpringer AnstreicherKMFampaMLeeJWilliamsJUsing continuous nonlinear relaxations to solve constrained maximum-entropy sampling problemsMath. Program. Ser. A199985221240170015710.1007/s101070050055 Hoffman, A., Lee, J., Williams, J.: New upper bounds for maximum-entropy sampling. In: mODa 6—Advances in Model-oriented Design and Analysis (Puchberg/Schneeberg, 2001), Contrib. Statist., pp. 143–153. Physica, Heidelberg (2001) LeeJWilliamsJA linear integer programming bound for maximum-entropy samplingMath. Program. Ser. B200394247256196911110.1007/s10107-002-0318-x LeeJElShaarawiAHPiegorschWWMaximum entropy samplingEncyclopedia of Environmetrics20122New YorkWiley15701574 Fiacco, A.V.: Introduction to sensitivity and stability analysis in nonlinear programming. Mathematics in Science and Engineering, vol. 165. Academic Press Inc, Orlando, FL (1983) FiaccoAVIshizukaYSensitivity and stability analysis for nonlinear programmingAnn. Oper. Res.1990271–4215235108899310.1007/BF02055196 TohK-CToddMJSDPT3: a Matlab software package for semidefinite programming, version 1.3Optim. Methods Softw.1999111–4545581177842910.1080/10556789908805762 KoC-WLeeJQueyranneMAn exact algorithm for maximum entropy samplingOper. Res.1995434684691135641610.1287/opre.43.4.684 Fiacco, A.V., McCormick, G.P.: Nonlinear Programming: Sequential Unconstrained Minimization Techniques. Wiley, New York (1968). Reprint: Volume 4 of SIAM Classics in Applied Mathematics, SIAM Publications, Philadelphia, PA 19104–2688, USA, 1990 Helmberg, C.: The ConicBundle Library for Convex Optimization. https://www-user.tu-chemnitz.de/~helmberg/ConicBundle/ (2005–2019) Anstreicher, K.M., Lee, J.: A masked spectral bound for maximum-entropy sampling. In: mODa 7—Advances in Model-oriented Design and Analysis, Contrib. Statist., pp. 1–12. Physica, Heidelberg (2004) TohK-CToddMJTütüncüRHAnjosMFLasserreJBOn the implementation and usage of sdpt3–a matlab software package for semidefinite-quadratic-linear programming, version 4.0Handbook on Semidefinite. Conic and Polynomial Optimization2012BostonSpringer71575410.1007/978-1-4614-0769-0_25 Anstreicher, K.M.: Efficient solution of maximum-entropy sampling problems. Oper. Res. (2020). DOI:https://doi.org/10.1287/opre.2019.1962(to appear) FischerIGruberGRendlFSotirovRComputational experience with a bundle approach for semidefinite cutting plane relaxations of max-cut and equipartitionMath. Program.2006105451469219083010.1007/s10107-005-0661-9 ShewryMCWynnHPMaximum entropy samplingJ. Appl. Stat.19874616517010.1080/02664768700000020 HornRAMatrix Analysis19851CambridgeCambridge University Press10.1017/CBO9780511810817 BurerSLeeJSolving maximum-entropy sampling problems using factored masksMath. Program. Ser. B2007109263281229514410.1007/s10107-006-0024-1 LeeJLindJGeneralized maximum-entropy samplingINFOR Inf. Syst. Oper. Res.2020581681814113660 Li, Y., Xie, W.: Best principal submatrix selection for the maximum entropy sampling problem: scalable algorithms and performance guarantees. Technical report, arXiv:2001.08537 (2020) AnstreicherKMMaximum-entropy sampling and the Boolean quadric polytopeJ. Global Optim.2018724603618387763210.1007/s10898-018-0662-x LeeJConstrained maximum-entropy samplingOper. Res.19984665566410.1287/opre.46.5.655 BoydSVandenbergheLConvex Optimization2004CambridgeCambridge University Press10.1017/CBO9780511804441 AnstreicherKMFampaMLeeJWilliamsJMaximum-entropy remote samplingDiscrete Appl. Math.20011083211226180791710.1016/S0166-218X(00)00217-1 BillionnetAElloumiSLambertAWiegeleAUsing a Conic Bundle method to accelerate both phases of a Quadratic Convex ReformulationINFORMS J. Comput.201729318331365381510.1287/ijoc.2016.0731 Anstreicher, K.M., Fampa, M., Lee, J., Williams, J.: Continuous relaxations for constrained maximum-entropy sampling. Integer programming and combinatorial optimization (Vancouver. BC, 1996), volume 1084 of Lecture Notes in Computer Science, pp. 234–248. Springer, Berlin (1996) Powell, M.J.D.: Some global convergence properties of a variable metric algorithm for minimization without exact line searches. In: Nonlinear Programming (Proc. Sympos., New York, 1975), pp. 53–72. SIAM–AMS Proc., Vol. IX (1976) LewisASOvertonMLNonsmooth optimization via quasi-Newton methodsMath. Program.2013141135163309728210.1007/s10107-012-0514-2 A Billionnet (1588_CR7) 2017; 29 J Lee (1588_CR22) 2020; 58 (1588_CR31) 2005 MC Shewry (1588_CR28) 1987; 46 I Fischer (1588_CR11) 2006; 105 1588_CR26 1588_CR27 1588_CR24 1588_CR1 K-C Toh (1588_CR29) 1999; 11 1588_CR6 KM Anstreicher (1588_CR3) 2001; 108 1588_CR4 AV Fiacco (1588_CR12) 1990; 27 S Burer (1588_CR8) 2007; 109 S Boyd (1588_CR9) 2004 M Bakonyi (1588_CR10) 2011 1588_CR18 J Lee (1588_CR21) 2012 1588_CR15 KM Anstreicher (1588_CR2) 1999; 85 1588_CR16 1588_CR13 J Lee (1588_CR25) 2003; 94 1588_CR14 KM Anstreicher (1588_CR5) 2018; 72 AS Lewis (1588_CR23) 2013; 141 RA Horn (1588_CR17) 1985 J Lee (1588_CR20) 1998; 46 C-W Ko (1588_CR19) 1995; 43 K-C Toh (1588_CR30) 2012
References_xml	– reference: LeeJLindJGeneralized maximum-entropy samplingINFOR Inf. Syst. Oper. Res.2020581681814113660 – reference: AnstreicherKMFampaMLeeJWilliamsJUsing continuous nonlinear relaxations to solve constrained maximum-entropy sampling problemsMath. Program. Ser. A199985221240170015710.1007/s101070050055 – reference: AnstreicherKMFampaMLeeJWilliamsJMaximum-entropy remote samplingDiscrete Appl. Math.20011083211226180791710.1016/S0166-218X(00)00217-1 – reference: HornRAMatrix Analysis19851CambridgeCambridge University Press10.1017/CBO9780511810817 – reference: Fiacco, A.V.: Introduction to sensitivity and stability analysis in nonlinear programming. Mathematics in Science and Engineering, vol. 165. Academic Press Inc, Orlando, FL (1983) – reference: Fiacco, A.V., McCormick, G.P.: Nonlinear Programming: Sequential Unconstrained Minimization Techniques. Wiley, New York (1968). Reprint: Volume 4 of SIAM Classics in Applied Mathematics, SIAM Publications, Philadelphia, PA 19104–2688, USA, 1990 – reference: Li, Y., Xie, W.: Best principal submatrix selection for the maximum entropy sampling problem: scalable algorithms and performance guarantees. Technical report, arXiv:2001.08537 (2020) – reference: Anstreicher, K.M., Fampa, M., Lee, J., Williams, J.: Continuous relaxations for constrained maximum-entropy sampling. Integer programming and combinatorial optimization (Vancouver. BC, 1996), volume 1084 of Lecture Notes in Computer Science, pp. 234–248. Springer, Berlin (1996) – reference: Anstreicher, K.M.: Efficient solution of maximum-entropy sampling problems. Oper. Res. (2020). DOI:https://doi.org/10.1287/opre.2019.1962(to appear) – reference: BoydSVandenbergheLConvex Optimization2004CambridgeCambridge University Press10.1017/CBO9780511804441 – reference: LeeJElShaarawiAHPiegorschWWMaximum entropy samplingEncyclopedia of Environmetrics20122New YorkWiley15701574 – reference: ZhangFThe Schur Complement and its Applications. Numerical Methods and Algorithms2005New YorkSpringer – reference: BakonyiMWoerdemanHJMatrix Completions, Moments, and Sums of Hermitian Squares2011PrincetonPrinceton University Press10.23943/princeton/9780691128894.001.0001 – reference: TohK-CToddMJTütüncüRHAnjosMFLasserreJBOn the implementation and usage of sdpt3–a matlab software package for semidefinite-quadratic-linear programming, version 4.0Handbook on Semidefinite. Conic and Polynomial Optimization2012BostonSpringer71575410.1007/978-1-4614-0769-0_25 – reference: Hoffman, A., Lee, J., Williams, J.: New upper bounds for maximum-entropy sampling. In: mODa 6—Advances in Model-oriented Design and Analysis (Puchberg/Schneeberg, 2001), Contrib. Statist., pp. 143–153. Physica, Heidelberg (2001) – reference: Helmberg, C.: The ConicBundle Library for Convex Optimization. https://www-user.tu-chemnitz.de/~helmberg/ConicBundle/ (2005–2019) – reference: BillionnetAElloumiSLambertAWiegeleAUsing a Conic Bundle method to accelerate both phases of a Quadratic Convex ReformulationINFORMS J. Comput.201729318331365381510.1287/ijoc.2016.0731 – reference: LewisASOvertonMLNonsmooth optimization via quasi-Newton methodsMath. Program.2013141135163309728210.1007/s10107-012-0514-2 – reference: ShewryMCWynnHPMaximum entropy samplingJ. Appl. Stat.19874616517010.1080/02664768700000020 – reference: BurerSLeeJSolving maximum-entropy sampling problems using factored masksMath. Program. Ser. B2007109263281229514410.1007/s10107-006-0024-1 – reference: Powell, M.J.D.: Some global convergence properties of a variable metric algorithm for minimization without exact line searches. In: Nonlinear Programming (Proc. Sympos., New York, 1975), pp. 53–72. SIAM–AMS Proc., Vol. IX (1976) – reference: TohK-CToddMJSDPT3: a Matlab software package for semidefinite programming, version 1.3Optim. Methods Softw.1999111–4545581177842910.1080/10556789908805762 – reference: KoC-WLeeJQueyranneMAn exact algorithm for maximum entropy samplingOper. Res.1995434684691135641610.1287/opre.43.4.684 – reference: FischerIGruberGRendlFSotirovRComputational experience with a bundle approach for semidefinite cutting plane relaxations of max-cut and equipartitionMath. Program.2006105451469219083010.1007/s10107-005-0661-9 – reference: AnstreicherKMMaximum-entropy sampling and the Boolean quadric polytopeJ. Global Optim.2018724603618387763210.1007/s10898-018-0662-x – reference: Anstreicher, K.M., Lee, J.: A masked spectral bound for maximum-entropy sampling. In: mODa 7—Advances in Model-oriented Design and Analysis, Contrib. Statist., pp. 1–12. Physica, Heidelberg (2004) – reference: FiaccoAVIshizukaYSensitivity and stability analysis for nonlinear programmingAnn. Oper. Res.1990271–4215235108899310.1007/BF02055196 – reference: Fedorov, V., Lee, J.: Design of experiments in statistics. In: Handbook of Semidefinite Programming, volume 27 of Internat. Ser. Oper. Res. Management Sci., pp. 511–532. Kluwer Acad. Publ., Boston, MA (2000) – reference: Löfberg, J.: Yalmip: A toolbox for modeling and optimization in Matlab. In: Proceedings of the CACSD Conference (2004) – reference: LeeJConstrained maximum-entropy samplingOper. Res.19984665566410.1287/opre.46.5.655 – reference: LeeJWilliamsJA linear integer programming bound for maximum-entropy samplingMath. Program. Ser. B200394247256196911110.1007/s10107-002-0318-x – ident: 1588_CR14 doi: 10.1007/978-1-4615-4381-7_17 – volume: 72 start-page: 603 issue: 4 year: 2018 ident: 1588_CR5 publication-title: J. Global Optim. doi: 10.1007/s10898-018-0662-x – ident: 1588_CR1 doi: 10.1007/3-540-61310-2_18 – volume: 46 start-page: 655 year: 1998 ident: 1588_CR20 publication-title: Oper. Res. doi: 10.1287/opre.46.5.655 – volume-title: Convex Optimization year: 2004 ident: 1588_CR9 doi: 10.1017/CBO9780511804441 – start-page: 1570 volume-title: Encyclopedia of Environmetrics year: 2012 ident: 1588_CR21 – volume: 46 start-page: 165 year: 1987 ident: 1588_CR28 publication-title: J. Appl. Stat. doi: 10.1080/02664768700000020 – start-page: 715 volume-title: Handbook on Semidefinite. Conic and Polynomial Optimization year: 2012 ident: 1588_CR30 doi: 10.1007/978-1-4614-0769-0_25 – volume: 108 start-page: 211 issue: 3 year: 2001 ident: 1588_CR3 publication-title: Discrete Appl. Math. doi: 10.1016/S0166-218X(00)00217-1 – volume-title: Matrix Completions, Moments, and Sums of Hermitian Squares year: 2011 ident: 1588_CR10 doi: 10.23943/princeton/9780691128894.001.0001 – volume: 105 start-page: 451 year: 2006 ident: 1588_CR11 publication-title: Math. Program. doi: 10.1007/s10107-005-0661-9 – ident: 1588_CR4 doi: 10.1007/978-3-7908-2693-7_1 – volume: 141 start-page: 135 year: 2013 ident: 1588_CR23 publication-title: Math. Program. doi: 10.1007/s10107-012-0514-2 – ident: 1588_CR6 doi: 10.1287/opre.2019.1962 – ident: 1588_CR13 – volume: 109 start-page: 263 year: 2007 ident: 1588_CR8 publication-title: Math. Program. Ser. B doi: 10.1007/s10107-006-0024-1 – volume: 58 start-page: 168 year: 2020 ident: 1588_CR22 publication-title: INFOR Inf. Syst. Oper. Res. – volume-title: The Schur Complement and its Applications. Numerical Methods and Algorithms year: 2005 ident: 1588_CR31 – volume: 43 start-page: 684 issue: 4 year: 1995 ident: 1588_CR19 publication-title: Oper. Res. doi: 10.1287/opre.43.4.684 – ident: 1588_CR27 – ident: 1588_CR18 doi: 10.1007/978-3-642-57576-1_16 – volume: 94 start-page: 247 year: 2003 ident: 1588_CR25 publication-title: Math. Program. Ser. B doi: 10.1007/s10107-002-0318-x – volume-title: Matrix Analysis year: 1985 ident: 1588_CR17 doi: 10.1017/CBO9780511810817 – volume: 11 start-page: 545 issue: 1–4 year: 1999 ident: 1588_CR29 publication-title: Optim. Methods Softw. doi: 10.1080/10556789908805762 – ident: 1588_CR15 doi: 10.1137/1.9781611971316 – volume: 29 start-page: 318 year: 2017 ident: 1588_CR7 publication-title: INFORMS J. Comput. doi: 10.1287/ijoc.2016.0731 – ident: 1588_CR24 – ident: 1588_CR16 – ident: 1588_CR26 – volume: 85 start-page: 221 year: 1999 ident: 1588_CR2 publication-title: Math. Program. Ser. A doi: 10.1007/s101070050055 – volume: 27 start-page: 215 issue: 1–4 year: 1990 ident: 1588_CR12 publication-title: Ann. Oper. Res. doi: 10.1007/BF02055196
SSID	ssj0001388
Score	2.427295
Snippet	The maximum-entropy sampling problem is a fundamental and challenging combinatorial-optimization problem, with application in spatial statistics. It asks to...
SourceID	hal proquest crossref springer
SourceType	Open Access Repository Aggregation Database Enrichment Source Index Database Publisher
StartPage	539
SubjectTerms	Calculus of Variations and Optimal Control; Optimization Combinatorial analysis Combinatorics Convexity Covariance matrix Entropy Exact solutions Full Length Paper Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Optimization Optimization and Control Sampling Theoretical Upper bounds
Title	Mixing convex-optimization bounds for maximum-entropy sampling
URI	https://link.springer.com/article/10.1007/s10107-020-01588-w https://www.proquest.com/docview/2552288734 https://hal.science/hal-03016397
Volume	188
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
link	http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LT8JAEN4oXPRgfEYUSWO86SbttlvKxaQoSFQ8SYKnZrvdVRIpxILgv3emtAWNmnhq2m4fmWln5tv9ZoaQM-HaylERo1boKgAooaSeJxSNdCilq5jL00pM3Qe303Nu-7yfJYUlOds9X5JMLfVKspuF02oMiVQc9DtbJ2UO2B2JXD3mF_bXsj0vb9SK0UGWKvPzPb64o_UXJEOuRJrfFkdTn9PeJltZsGj4C-3ukDUV75LNlRKCsNct6q4me-SyO5jDYSPlks_pCOzBMEu0NEJsoJQYEKQaQzEfDKdDijO7o_GHkQjklcfP-6TXbj1edWjWIYFKiCMm1NZRQ4ODb2iuQRCONOuaK1MK0xNCalaPPCbAyze44-iICxA9aIxrpqVpaQCnB6QUj2J1SAwsJCciJpSqA8ZiLuAgEVq2NAFyaNd1KsTKBRXIrHw4drF4DZaFj1G4AQg3SIUbzCrkvLhmvCie8efoU5B_MRDrXnf8-wCPIW7DFch3q0KquXqC7G9LAoBFjIG1tOEtL3KVLU___sij_w0_JhsMKS0p_69KSpO3qTqBmGQS1kjZb14327i9ebpr1dJP8hPEeNoZ
linkProvider	Springer Nature
linkToHtml	http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1LT8JAEJ4AHtSD8RlR1MboSZu02wfloAlRCcjjBAm3dbvdVRJ5xILA__GHOltaQKMmHjh2u223M7sz8-3OA-CCuZawRUB003cFAhSf657HhB5In3NXENeJMjHVG265ZT-2nXYKPpJYmMjbPTmSjCT1UrCbqbbViHKkcpC_49iVsiqmYwRq4U3lHrl6SUjpoXlX1uNaAjpHjTvULRkUJKrCgnQkqlSbG3npCIMzw2OMS5IPPMJQHxYc25aBw3CQ-G-OJJIbpkQYh-9NwxoaH55aOy1SnMt70_K8pDCsskbi0Jyfx_xF_aVflPPlkmX77TA20nGlbdiKjVOtOJtNO5ASvV3YXEpZiFf1eZ7XcA9u650JNmuR7_pE76P86caBnZqvCjaFGhrFWpdNOt1RV1c7yf3BVAuZ8mPvPe9DayVUPIBMr98Th6CpxHUsIEyIPGI64iLuYr5pcQMhjnRdOwtmQijK43TlqmrGK10kWlbEpUhcGhGXjrNwNX9mMEvW8Wfvc6T_vKPKs10u1qhqUzhRnXi-m1nIJeyh8eoOKcIwQlA6WzjK64Rli9u_f_Lof93PYL3crNdordKoHsMGUe40ke9hDjLDt5E4QXto6J9G01GDp1XP_09OZRSt
linkToPdf	http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1LT8MwDLYGSAgOiKcYzwrBCSra9LHuANLEmMZjiAOTuIU0TWAS6yY62PhX_ETsrh0DARIHjk3TNrWT2F9ifwHYFb6jXBUx0w59hQAllGYQCGVGOpTSV8z3UiamxpVfb7rnt95tAd7yXJg02j3fkhzmNBBLU9w77Eb6cCzxzaYlNkZBVR7qup-FVV6o1z6CtuTorIoa3mOsdnpzUjezcwVMida3Zzo6Kms0i2XtaTSvrrRK2lOWFFYghNSsFAVMoG0se66rI09gg_E_Pc20tGyNkA7fOwFTLmUf4whqsspo7redIMgPiSXPJEvT-b7Nn0zhxAMFYo55uV82ZlN7V5uHucxRNSrDnrUABRUvwuwYfSFeNUacr8kSHDdaAyw20jj2gdnBuaidJXkaIR3elBjoIBttMWi1n9smrSp3uq9GIiimPb5fhua_SHEFJuNOrFbBIBI7ETGhVAnxHfMRg4nQdqSFcEf7vlsEOxcUlxl1OZ2g8cg_SJdJuByFy1Ph8n4R9kfPdIfEHb_W3kH5jyoS53a9csmpjDAj7X6-2EXYyNXDs5GecIRkjOFM7WArD3KVfdz--ZNrf6u-DdPX1Rq_PLu6WIcZRpE1aRjiBkz2np7VJrpGvXAr7Y0G3P13938HjegY4A
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=Mixing+convex-optimization+bounds+for+maximum-entropy+sampling&rft.jtitle=Mathematical+programming&rft.au=Chen%2C+Zhongzhu&rft.au=Fampa%2C+Marcia&rft.au=Lambert%2C+Am%C3%A9lie&rft.au=Lee%2C+Jon&rft.date=2021-08-01&rft.issn=0025-5610&rft.eissn=1436-4646&rft.volume=188&rft.issue=2&rft.spage=539&rft.epage=568&rft_id=info:doi/10.1007%2Fs10107-020-01588-w&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s10107_020_01588_w
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