New horizons in sphere-packing theory, part II: lattice-based derivative-free optimization via global surrogates

Derivative-free algorithms are frequently required for the optimization of nonsmooth scalar functions in n dimensions resulting, for example, from physical experiments or from the statistical averaging of numerical simulations of chaotic systems such as turbulent flows. The core idea of all efficien...

Celý popis

Uložené v:

Podrobná bibliografia
Vydané v:	Journal of global optimization Ročník 56; číslo 1; s. 61 - 91
Hlavní autori:	Belitz, Paul, Bewley, Thomas
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Boston Springer US 01.05.2013 Springer Springer Nature B.V
Predmet:	Algorithms Analysis Approximation Computer Science Global Positioning System Mathematics Mathematics and Statistics Methods Numerical analysis Operations Research/Decision Theory Optimization Optimization algorithms Packing problem Pattern recognition Real Functions Simplex method Simulation Studies Trends Turbulence Generalized pattern search Global optimization Surrogate-based methods N-dimensional sphere-packing theory Kriging interpolation Derivative-free optimization
ISSN:	0925-5001, 1573-2916
On-line prístup:	Získať plný text
Tagy:	Pridať tag Žiadne tagy, Buďte prvý, kto otaguje tento záznam!

Abstract	Derivative-free algorithms are frequently required for the optimization of nonsmooth scalar functions in n dimensions resulting, for example, from physical experiments or from the statistical averaging of numerical simulations of chaotic systems such as turbulent flows. The core idea of all efficient algorithms for problems of this type is to keep function evaluations far apart until convergence is approached. Generalized pattern search ( GPS ) algorithms, a modern class of methods particularly well suited to such problems, accomplish this by coordinating the search with an underlying grid which is refined, and coarsened, as appropriate. One of the most efficient subclasses of GPS algorithms, known as the surrogate management framework ( SMF ; see Booker et al. in Struct Multidiscip Optim 17:1–13, 1999 ), alternates between an exploratory search over an interpolating function which summarizes the trends exhibited by existing function evaluations, and an exhaustive poll which checks the function on neighboring points to confirm or confute the local optimality of any given candidate minimum point ( CMP ) on the underlying grid. The original SMF algorithm implemented a GPS step on an underlying Cartesian grid, augmented with a Kriging-based surrogate search. Rather than using the n -dimensional Cartesian grid (the typical choice), the present work introduces for this purpose the use of lattices derived from n -dimensional sphere packings. As reviewed and analyzed extensively in Part I of this series (see Belitz, PhD dissertation, University of California, San Diego, 2011 , Chap. 2), such lattices are significantly more uniform and have many more nearest neighbors than their Cartesian counterparts. Both of these facts make them far better suited for coordinating GPS algorithms, as demonstrated here in a variety of numerical tests.
AbstractList	Derivative-free algorithms are frequently required for the optimization of nonsmooth scalar functions in n dimensions resulting, for example, from physical experiments or from the statistical averaging of numerical simulations of chaotic systems such as turbulent flows. The core idea of all efficient algorithms for problems of this type is to keep function evaluations far apart until convergence is approached. Generalized pattern search ( GPS ) algorithms, a modern class of methods particularly well suited to such problems, accomplish this by coordinating the search with an underlying grid which is refined, and coarsened, as appropriate. One of the most efficient subclasses of GPS algorithms, known as the surrogate management framework ( SMF ; see Booker et al. in Struct Multidiscip Optim 17:1–13, 1999 ), alternates between an exploratory search over an interpolating function which summarizes the trends exhibited by existing function evaluations, and an exhaustive poll which checks the function on neighboring points to confirm or confute the local optimality of any given candidate minimum point ( CMP ) on the underlying grid. The original SMF algorithm implemented a GPS step on an underlying Cartesian grid, augmented with a Kriging-based surrogate search. Rather than using the n -dimensional Cartesian grid (the typical choice), the present work introduces for this purpose the use of lattices derived from n -dimensional sphere packings. As reviewed and analyzed extensively in Part I of this series (see Belitz, PhD dissertation, University of California, San Diego, 2011 , Chap. 2), such lattices are significantly more uniform and have many more nearest neighbors than their Cartesian counterparts. Both of these facts make them far better suited for coordinating GPS algorithms, as demonstrated here in a variety of numerical tests. Derivative-free algorithms are frequently required for the optimization of nonsmooth scalar functions in n dimensions resulting, for example, from physical experiments or from the statistical averaging of numerical simulations of chaotic systems such as turbulent flows. The core idea of all efficient algorithms for problems of this type is to keep function evaluations far apart until convergence is approached. Generalized pattern search (GPS) algorithms, a modern class of methods particularly well suited to such problems, accomplish this by coordinating the search with an underlying grid which is refined, and coarsened, as appropriate. One of the most efficient subclasses of GPS algorithms, known as the surrogate management framework (SMF; see Booker et al. in Struct Multidiscip Optim 17:1-13, 1999), alternates between an exploratory search over an interpolating function which summarizes the trends exhibited by existing function evaluations, and an exhaustive poll which checks the function on neighboring points to confirm or confute the local optimality of any given candidate minimum point (CMP) on the underlying grid. The original SMF algorithm implemented a GPS step on an underlying Cartesian grid, augmented with a Kriging-based surrogate search. Rather than using the n-dimensional Cartesian grid (the typical choice), the present work introduces for this purpose the use of lattices derived from n-dimensional sphere packings. As reviewed and analyzed extensively in Part I of this series (see Belitz, PhD dissertation, University of California, San Diego, 2011, Chap. 2), such lattices are significantly more uniform and have many more nearest neighbors than their Cartesian counterparts. Both of these facts make them far better suited for coordinating GPS algorithms, as demonstrated here in a variety of numerical tests. Derivative-free algorithms are frequently required for the optimization of nonsmooth scalar functions in n dimensions resulting, for example, from physical experiments or from the statistical averaging of numerical simulations of chaotic systems such as turbulent flows. The core idea of all efficient algorithms for problems of this type is to keep function evaluations far apart until convergence is approached. Generalized pattern search (GPS) algorithms, a modern class of methods particularly well suited to such problems, accomplish this by coordinating the search with an underlying grid which is refined, and coarsened, as appropriate. One of the most efficient subclasses of GPS algorithms, known as the surrogate management framework (SMF; see Booker et al. in Struct Multidiscip Optim 17:1-13, 1999), alternates between an exploratory search over an interpolating function which summarizes the trends exhibited by existing function evaluations, and an exhaustive poll which checks the function on neighboring points to confirm or confute the local optimality of any given candidate minimum point (CMP) on the underlying grid. The original SMF algorithm implemented a GPS step on an underlying Cartesian grid, augmented with a Kriging-based surrogate search. Rather than using the n-dimensional Cartesian grid (the typical choice), the present work introduces for this purpose the use of lattices derived from n-dimensional sphere packings. As reviewed and analyzed extensively in Part I of this series (see Belitz, PhD dissertation, University of California, San Diego, 2011, Chap. 2), such lattices are significantly more uniform and have many more nearest neighbors than their Cartesian counterparts. Both of these facts make them far better suited for coordinating GPS algorithms, as demonstrated here in a variety of numerical tests. Keywords N-dimensional sphere-packing theory * Generalized pattern search * Derivative-free optimization * Global optimization * Surrogate-based methods * Kriging interpolation Derivative-free algorithms are frequently required for the optimization of nonsmooth scalar functions in n dimensions resulting, for example, from physical experiments or from the statistical averaging of numerical simulations of chaotic systems such as turbulent flows. The core idea of all efficient algorithms for problems of this type is to keep function evaluations far apart until convergence is approached. Generalized pattern search (GPS) algorithms, a modern class of methods particularly well suited to such problems, accomplish this by coordinating the search with an underlying grid which is refined, and coarsened, as appropriate. One of the most efficient subclasses of GPS algorithms, known as the surrogate management framework (SMF; see Booker etÂ al. in Struct Multidiscip Optim 17:1â[euro]"13, 1999 ), alternates between an exploratory search over an interpolating function which summarizes the trends exhibited by existing function evaluations, and an exhaustive poll which checks the function on neighboring points to confirm or confute the local optimality of any given candidate minimum point (CMP) on the underlying grid. The original SMF algorithm implemented a GPS step on an underlying Cartesian grid, augmented with a Kriging-based surrogate search. Rather than using the n-dimensional Cartesian grid (the typical choice), the present work introduces for this purpose the use of lattices derived from n-dimensional sphere packings. As reviewed and analyzed extensively in Part I of this series (see Belitz, PhD dissertation, University of California, San Diego, 2011 , Chap. 2), such lattices are significantly more uniform and have many more nearest neighbors than their Cartesian counterparts. Both of these facts make them far better suited for coordinating GPS algorithms, as demonstrated here in a variety of numerical tests.[PUBLICATION ABSTRACT]
Audience	Academic
Author	Belitz, Paul Bewley, Thomas
Author_xml	– sequence: 1 givenname: Paul surname: Belitz fullname: Belitz, Paul organization: Flow Control & Coordinated Robotics Labs, UC San Diego – sequence: 2 givenname: Thomas surname: Bewley fullname: Bewley, Thomas email: bewley@ucsd.edu organization: Flow Control & Coordinated Robotics Labs, UC San Diego
BookMark	eNp9kU1v1DAQhi1UJLaFH8DNEhcOuPgjsR1uVQV0pQoucLacZJx1ydrB9i5qfz3ehgOqBPLB0uh9PDN-ztFZiAEQes3oJaNUvc-M6k4TyjjptJREPUMb1ipBeMfkGdrQjrekpZS9QOc531FKO93yDVq-wC-8i8k_xJCxDzgvO0hAFjv88GHCZQcx3b_Di00Fb7cf8GxL8QOQ3mYY8QjJH23xRyAuAeC4FL_3D7USAz56i6c59nbG-ZBSnGyB_BI9d3bO8OrPfYG-f_r47fqG3H79vL2-uiWD0LoQx0arHeOUAwg1aiGbtu9HBw5GJ6UVvdAwSleXaLp-aBsKolO671WjobFcXKC367tLij8PkIvZ-zzAPNsA8ZANa6kUbUeVqtE3T6J38ZBCnc4wwYUUnDaipi7X1GRnMD64WJId6hlh74dqw_lav1INb7VkHa0AW4EhxZwTOLMkv7fp3jBqTtLMKs1UaeYkzZxGUU-YwZfH36zN_Pxfkq9krl3CBOmvJf4J_QZWLK6y
CitedBy_id	crossref_primary_10_1007_s10898_019_00854_2 crossref_primary_10_1016_j_ymssp_2023_110401 crossref_primary_10_1007_s10898_015_0384_2 crossref_primary_10_1088_1742_5468_ad0223 crossref_primary_10_1016_j_ymssp_2024_112259 crossref_primary_10_1088_1742_5468_2016_11_113301 crossref_primary_10_1007_s10898_014_0174_2 crossref_primary_10_1007_s10898_017_0548_3 crossref_primary_10_1017_S0962492919000060 crossref_primary_10_1007_s10898_016_0433_5
Cites_doi	10.1080/00401706.1962.10490033 10.1007/978-3-322-98556-9 10.1007/978-3-642-61370-8 10.1017/S0022112006003235 10.1007/BF02095633 10.1115/1.3653121 10.1093/comjnl/7.4.308 10.1137/080716980 10.1109/21.23094 10.1137/S1052623499354989 10.1137/S1052623493250780 10.2113/gsecongeo.58.8.1246 10.1007/BF01099263 10.1023/A:1012771025575 10.1080/14786440409463107 10.1007/BF01197708 10.1109/ICSMC.1991.169748 10.1109/ICSMC.1992.271711 10.1137/040603371 10.1126/science.220.4598.671 10.1109/ICNN.1995.488968
ContentType	Journal Article
Copyright	Springer Science+Business Media, LLC. 2012 COPYRIGHT 2022 Springer Springer Science+Business Media New York 2013
Copyright_xml	– notice: Springer Science+Business Media, LLC. 2012 – notice: COPYRIGHT 2022 Springer – notice: Springer Science+Business Media New York 2013
DBID	AAYXX CITATION 3V. 7SC 7WY 7WZ 7XB 87Z 88I 8AL 8AO 8FD 8FE 8FG 8FK 8FL 8G5 ABJCF ABUWG AFKRA ARAPS AZQEC BENPR BEZIV BGLVJ CCPQU DWQXO FRNLG F~G GNUQQ GUQSH HCIFZ JQ2 K60 K6~ K7- L.- L.0 L6V L7M L~C L~D M0C M0N M2O M2P M7S MBDVC P5Z P62 PHGZM PHGZT PKEHL PQBIZ PQBZA PQEST PQGLB PQQKQ PQUKI PRINS PTHSS Q9U
DOI	10.1007/s10898-012-9866-7
DatabaseName	CrossRef ProQuest Central (Corporate) Computer and Information Systems Abstracts ProQuest 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) Research Library (Alumni) Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest Central UK/Ireland Advanced Technologies & Aerospace Database‎ (1962 - current) ProQuest Central Essentials - QC ProQuest Central Business Premium Collection Technology collection ProQuest One Community College ProQuest Central Business Premium Collection (Alumni) ABI/INFORM Global (Corporate) ProQuest Central Student ProQuest Research Library SciTech Premium Collection ProQuest Computer Science Collection ProQuest Business Collection (Alumni Edition) ProQuest Business Collection Computer Science Database ABI/INFORM Professional Advanced ABI/INFORM Professional Standard ProQuest Engineering Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional ABI/INFORM Global Computing Database Research Library Science Database Engineering Database Research Library (Corporate) 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) Research Library Prep 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 Research Library (Alumni Edition) ProQuest Pharma Collection ProQuest Central ABI/INFORM Professional Advanced ProQuest Engineering Collection ABI/INFORM Professional Standard ProQuest Central Korea ProQuest Research Library 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 Sciences (General) Computer Science
EISSN	1573-2916
EndPage	91
ExternalDocumentID	2936184251 A742586190 10_1007_s10898_012_9866_7
Genre	Feature
GroupedDBID	-52 -57 -5G -BR -EM -Y2 -~C .4S .86 .DC .VR 06D 0R~ 0VY 199 1N0 1SB 2.D 203 28- 29K 2J2 2JN 2JY 2KG 2LR 2P1 2VQ 2~H 30V 3V. 4.4 406 408 409 40D 40E 5GY 5QI 5VS 67Z 6NX 78A 7WY 88I 8AO 8FE 8FG 8FL 8G5 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYOK AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDZT ABECU ABFTV ABHLI ABHQN ABJCF ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTAH ABTEG ABTHY ABTKH ABTMW ABULA ABUWG ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACGOD ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACZOJ ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE 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 AHSBF AHYZX AI. AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARAPS ARCSS ARMRJ ASPBG AVWKF AXYYD AYQZM AZFZN AZQEC B-. BA0 BAPOH BBWZM BDATZ BENPR BEZIV BGLVJ BGNMA BPHCQ BSONS CAG CCPQU COF CS3 CSCUP D-I DDRTE DL5 DNIVK DPUIP DU5 DWQXO EBLON EBS EDO EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRNLG FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNUQQ GNWQR GQ6 GQ7 GQ8 GROUPED_ABI_INFORM_COMPLETE GUQSH GXS H13 HCIFZ HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I09 IAO IHE IJ- IKXTQ ITC ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ K60 K6V K6~ K7- KDC KOV KOW L6V LAK LLZTM M0C M0N M2O M2P M4Y M7S MA- N2Q N9A NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM OVD P19 P2P P62 P9M PF0 PQBIZ PQBZA PQQKQ PROAC PT4 PT5 PTHSS Q2X QOK QOS R4E R89 R9I RHV RNI RNS ROL RPX RSV RZC RZE RZK S16 S1Z S26 S27 S28 S3B SAP SBE SCLPG SDD SDH SDM SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TEORI TN5 TSG TSK TSV TUC TUS U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW VH1 W23 W48 WK8 YLTOR Z45 Z5O Z7R Z7X Z7Z Z81 Z83 Z86 Z88 Z8M Z8N Z8T Z8U Z8W Z92 ZMTXR ZWQNP ZY4 ~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.- L.0 L7M L~C L~D MBDVC PKEHL PQEST PQUKI PRINS Q9U
ID	FETCH-LOGICAL-c388t-f1da8f1202ee37d83645bbdfefedf66a3b38ed6f85249bc540e3978bb748e4a23
IEDL.DBID	K7-
ISICitedReferencesCount	9
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000317079100004&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	0925-5001
IngestDate	Sun Nov 09 13:38:34 EST 2025 Tue Nov 04 21:12:37 EST 2025 Sat Nov 29 09:57:27 EST 2025 Sat Nov 29 01:59:30 EST 2025 Tue Nov 18 22:37:13 EST 2025 Fri Feb 21 02:42:30 EST 2025
IsPeerReviewed	true
IsScholarly	true
Issue	1
Keywords	Generalized pattern search Global optimization Surrogate-based methods N-dimensional sphere-packing theory Kriging interpolation Derivative-free optimization
Language	English
License	http://www.springer.com/tdm
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c388t-f1da8f1202ee37d83645bbdfefedf66a3b38ed6f85249bc540e3978bb748e4a23
Notes	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23
PQID	1323632043
PQPubID	29930
PageCount	31
ParticipantIDs	proquest_miscellaneous_1506359077 proquest_journals_1323632043 gale_infotracacademiconefile_A742586190 crossref_primary_10_1007_s10898_012_9866_7 crossref_citationtrail_10_1007_s10898_012_9866_7 springer_journals_10_1007_s10898_012_9866_7
PublicationCentury	2000
PublicationDate	2013-05-01
PublicationDateYYYYMMDD	2013-05-01
PublicationDate_xml	– month: 05 year: 2013 text: 2013-05-01 day: 01
PublicationDecade	2010
PublicationPlace	Boston
PublicationPlace_xml	– name: Boston – name: Dordrecht
PublicationSubtitle	An International Journal Dealing with Theoretical and Computational Aspects of Seeking Global Optima and Their Applications in Science, Management and Engineering
PublicationTitle	Journal of global optimization
PublicationTitleAbbrev	J Glob Optim
PublicationYear	2013
Publisher	Springer US Springer Springer Nature B.V
Publisher_xml	– name: Springer US – name: Springer – name: Springer Nature B.V
References	Isaaks, Srivastav (CR12) 1989 Kushner (CR17) 1964; 86 Rasmussen, Williams (CR25) 2006 Thomson (CR29) 1904; 7 Marsden, Vignon-Clementel, Chan, Feinstein, Tyalor (CR18) 2007; 572 Booker, Dennis, Frank, Serafini, Torczon, Trosset (CR4) 1999; 17 McKay, Beckman, Conover (CR20) 1979; 21 Spendley, Hext, Himsworth (CR26) 1962; 4 CR14 Fejes Tóth (CR10) 1971; 1 Abramson, Audet, Dennis, Le Digabel (CR1) 2008; 20 Goldberg (CR11) 1989 Kirkpatrick, Gelatt, Vecchi (CR15) 1984; 20 Cox, John, Alexandrov, Hussaini (CR7) 1997 Torczon (CR30) 1997; 7 Conway, Sloane (CR5) 1998 Ermoliev (CR9) 1988 Torn, Zilinskas (CR31) 1987 Matheron (CR19) 1963; 58 CR2 Krige (CR16) 1951 Tammes (CR28) 1930; 27 CR3 Coope, Price (CR6) 2001; 11 CR8 CR24 Jones (CR13) 2001; 21 Yang, Feinstein, Marsden (CR32) 2010; 199 Nelder, Mead (CR23) 1965; 7 Stuckman (CR27) 1988; 18 Mockus (CR22) 1994; 4 Meschkowski (CR21) 1960 9866_CR8 H. Meschkowski (9866_CR21) 1960 J.A. Nelder (9866_CR23) 1965; 7 Y. Ermoliev (9866_CR9) 1988 P.M.L. Tammes (9866_CR28) 1930; 27 9866_CR2 J.J. Thomson (9866_CR29) 1904; 7 I.D. Coope (9866_CR6) 2001; 11 D.G. Krige (9866_CR16) 1951 9866_CR3 M.D. McKay (9866_CR20) 1979; 21 C.E. Rasmussen (9866_CR25) 2006 B.E. Stuckman (9866_CR27) 1988; 18 W. Yang (9866_CR32) 2010; 199 L. Fejes Tóth (9866_CR10) 1971; 1 W. Spendley (9866_CR26) 1962; 4 M.A. Abramson (9866_CR1) 2008; 20 H.J. Kushner (9866_CR17) 1964; 86 9866_CR24 V. Torczon (9866_CR30) 1997; 7 D.R. Jones (9866_CR13) 2001; 21 A. Booker (9866_CR4) 1999; 17 A. Torn (9866_CR31) 1987 D.D. Cox (9866_CR7) 1997 E.H. Isaaks (9866_CR12) 1989 J. Mockus (9866_CR22) 1994; 4 A.L. Marsden (9866_CR18) 2007; 572 S. Kirkpatrick (9866_CR15) 1984; 20 J.H. Conway (9866_CR5) 1998 D.E. Goldberg (9866_CR11) 1989 9866_CR14 G. Matheron (9866_CR19) 1963; 58
References_xml	– volume: 4 start-page: 441 year: 1962 end-page: 461 ident: CR26 article-title: Sequential application of simplex designs in optimisation and evolutionary operation publication-title: Technometrics doi: 10.1080/00401706.1962.10490033 – year: 1960 ident: CR21 publication-title: Ungelöste und unlösbare Probleme der Geometrie doi: 10.1007/978-3-322-98556-9 – year: 1988 ident: CR9 publication-title: Numerical Techniques for Stochastic Optimization doi: 10.1007/978-3-642-61370-8 – volume: 572 start-page: 250 year: 2007 end-page: 263 ident: CR18 article-title: Trailing-edge noise reduction using derivative-free optimization and large-eddy simulation publication-title: J. Fluid Mech. doi: 10.1017/S0022112006003235 – volume: 1 start-page: 25 year: 1971 end-page: 33 ident: CR10 article-title: Perfect distribution of points on a sphere publication-title: Periodica Mathematica Hungarica doi: 10.1007/BF02095633 – volume: 86 start-page: 97 year: 1964 end-page: 106 ident: CR17 article-title: A new method of locating the maximum point of an arbitrary multipeak curve in the presence of noise publication-title: J. Basic Eng. doi: 10.1115/1.3653121 – ident: CR14 – year: 1987 ident: CR31 publication-title: Global Optimization – volume: 199 start-page: 2135 year: 2010 end-page: 2149 ident: CR32 article-title: Constrained optimization of an idealized Y-shaped baffle for the Fontan surgery at rest and exercise publication-title: CMAME – ident: CR2 – start-page: 315 year: 1997 end-page: 329 ident: CR7 article-title: SDO: a statistical method for global optimization publication-title: Multidisciplinary Design Optimization: State of the Art – volume: 7 start-page: 308 year: 1965 end-page: 313 ident: CR23 article-title: A simplex method for function minimization publication-title: Comput. J. doi: 10.1093/comjnl/7.4.308 – year: 1951 ident: CR16 publication-title: A statistical approach to some mine valuations and allied problems at the Witwatersrand – volume: 20 start-page: 948 year: 2008 end-page: 966 ident: CR1 article-title: OrthoMads: a deterministic Mads instance with orthogonal directions publication-title: SIAM J. Optim doi: 10.1137/080716980 – year: 1989 ident: CR11 publication-title: Genetic Algorithms in Search, Optimization, and Machine Learning – volume: 18 start-page: 965 year: 1988 end-page: 977 ident: CR27 article-title: A global search method for optimizing nonlinear systems publication-title: IEEE Trans. Syst. Man Cybern. doi: 10.1109/21.23094 – volume: 11 start-page: 859 year: 2001 end-page: 869 ident: CR6 article-title: On the convergence of grid-based methods for unconstrained optimization publication-title: SIAM J. Optim. doi: 10.1137/S1052623499354989 – ident: CR8 – volume: 7 start-page: 1 year: 1997 end-page: 25 ident: CR30 article-title: On the convergence of pattern search algorithms publication-title: SIAM J. Optim. doi: 10.1137/S1052623493250780 – year: 1989 ident: CR12 publication-title: An Introduction to Applied Geostatistics – volume: 20 start-page: 671 issue: 4598 year: 1984 end-page: 680 ident: CR15 article-title: Optimization vi simulated annealing publication-title: Science – volume: 58 start-page: 1246 year: 1963 end-page: 1266 ident: CR19 article-title: Principles of geostatistics publication-title: Econ. Geol. doi: 10.2113/gsecongeo.58.8.1246 – volume: 4 start-page: 347 year: 1994 end-page: 365 ident: CR22 article-title: Application of Bayesian approach to numerical methods of global and stochastic optimization publication-title: J. Global Optim. doi: 10.1007/BF01099263 – ident: CR3 – year: 2006 ident: CR25 publication-title: Gaussian Processes for Machine Learning – year: 1998 ident: CR5 publication-title: Sphere Packings, Lattices, and Groups – volume: 21 start-page: 345 year: 2001 end-page: 383 ident: CR13 article-title: A taxonomy of global optimization methods based on response surfaces publication-title: J. Global Optim. doi: 10.1023/A:1012771025575 – volume: 27 start-page: 1 year: 1930 end-page: 84 ident: CR28 article-title: On the origin of number and arrangement of the places of exit on the surface of pollen-grains publication-title: Recueil des travaux botaniques néerlandais – volume: 21 start-page: 239 year: 1979 end-page: 245 ident: CR20 article-title: A comparison of three methods for selecting values of input variables in the analysis of output from a computer code publication-title: Techonometrics – volume: 7 start-page: 237 issue: 39 year: 1904 end-page: 265 ident: CR29 article-title: On the structure of the atom: an investigation of the stability and periods of oscillation of a number of corpuscles arranged at equal intervals around the circumference of a circle; with application of the results to the theory of atomic structure publication-title: Philos. Mag. Ser. 6 doi: 10.1080/14786440409463107 – volume: 17 start-page: 1 year: 1999 end-page: 13 ident: CR4 article-title: A rigorous framework for optimization of expensive functions by surrogates publication-title: Struct. Multidiscip. Optim. doi: 10.1007/BF01197708 – ident: CR24 – volume-title: Gaussian Processes for Machine Learning year: 2006 ident: 9866_CR25 – volume: 17 start-page: 1 year: 1999 ident: 9866_CR4 publication-title: Struct. Multidiscip. Optim. doi: 10.1007/BF01197708 – volume: 7 start-page: 1 year: 1997 ident: 9866_CR30 publication-title: SIAM J. Optim. doi: 10.1137/S1052623493250780 – ident: 9866_CR24 doi: 10.1109/ICSMC.1991.169748 – start-page: 315 volume-title: Multidisciplinary Design Optimization: State of the Art year: 1997 ident: 9866_CR7 – volume-title: Genetic Algorithms in Search, Optimization, and Machine Learning year: 1989 ident: 9866_CR11 – ident: 9866_CR8 doi: 10.1109/ICSMC.1992.271711 – volume-title: Sphere Packings, Lattices, and Groups year: 1998 ident: 9866_CR5 – volume: 21 start-page: 345 year: 2001 ident: 9866_CR13 publication-title: J. Global Optim. doi: 10.1023/A:1012771025575 – volume: 199 start-page: 2135 year: 2010 ident: 9866_CR32 publication-title: CMAME – ident: 9866_CR2 doi: 10.1137/040603371 – volume-title: Global Optimization year: 1987 ident: 9866_CR31 – volume: 18 start-page: 965 year: 1988 ident: 9866_CR27 publication-title: IEEE Trans. Syst. Man Cybern. doi: 10.1109/21.23094 – volume: 11 start-page: 859 year: 2001 ident: 9866_CR6 publication-title: SIAM J. Optim. doi: 10.1137/S1052623499354989 – volume: 20 start-page: 671 issue: 4598 year: 1984 ident: 9866_CR15 publication-title: Science doi: 10.1126/science.220.4598.671 – volume: 1 start-page: 25 year: 1971 ident: 9866_CR10 publication-title: Periodica Mathematica Hungarica doi: 10.1007/BF02095633 – volume: 58 start-page: 1246 year: 1963 ident: 9866_CR19 publication-title: Econ. Geol. doi: 10.2113/gsecongeo.58.8.1246 – volume: 7 start-page: 308 year: 1965 ident: 9866_CR23 publication-title: Comput. J. doi: 10.1093/comjnl/7.4.308 – ident: 9866_CR14 doi: 10.1109/ICNN.1995.488968 – volume-title: Ungelöste und unlösbare Probleme der Geometrie year: 1960 ident: 9866_CR21 doi: 10.1007/978-3-322-98556-9 – volume-title: Numerical Techniques for Stochastic Optimization year: 1988 ident: 9866_CR9 doi: 10.1007/978-3-642-61370-8 – volume: 4 start-page: 441 year: 1962 ident: 9866_CR26 publication-title: Technometrics doi: 10.1080/00401706.1962.10490033 – volume: 572 start-page: 250 year: 2007 ident: 9866_CR18 publication-title: J. Fluid Mech. doi: 10.1017/S0022112006003235 – volume-title: An Introduction to Applied Geostatistics year: 1989 ident: 9866_CR12 – volume: 21 start-page: 239 year: 1979 ident: 9866_CR20 publication-title: Techonometrics – volume: 7 start-page: 237 issue: 39 year: 1904 ident: 9866_CR29 publication-title: Philos. Mag. Ser. 6 doi: 10.1080/14786440409463107 – volume: 86 start-page: 97 year: 1964 ident: 9866_CR17 publication-title: J. Basic Eng. doi: 10.1115/1.3653121 – volume-title: A statistical approach to some mine valuations and allied problems at the Witwatersrand year: 1951 ident: 9866_CR16 – volume: 27 start-page: 1 year: 1930 ident: 9866_CR28 publication-title: Recueil des travaux botaniques néerlandais – volume: 20 start-page: 948 year: 2008 ident: 9866_CR1 publication-title: SIAM J. Optim doi: 10.1137/080716980 – ident: 9866_CR3 – volume: 4 start-page: 347 year: 1994 ident: 9866_CR22 publication-title: J. Global Optim. doi: 10.1007/BF01099263
SSID	ssj0009852
Score	2.0435426
Snippet	Derivative-free algorithms are frequently required for the optimization of nonsmooth scalar functions in n dimensions resulting, for example, from physical... Derivative-free algorithms are frequently required for the optimization of nonsmooth scalar functions in n dimensions resulting, for example, from physical...
SourceID	proquest gale crossref springer
SourceType	Aggregation Database Enrichment Source Index Database Publisher
StartPage	61
SubjectTerms	Algorithms Analysis Approximation Computer Science Global Positioning System Mathematics Mathematics and Statistics Methods Numerical analysis Operations Research/Decision Theory Optimization Optimization algorithms Packing problem Pattern recognition Real Functions Simplex method Simulation Studies Trends Turbulence
SummonAdditionalLinks	– databaseName: SpringerLINK Contemporary 1997-Present dbid: RSV link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1bi9QwFD7o6oM-uO6oOLpKBMFroG3a9NS3RVxc0EW8LPsWcisOrO3Qzgzor_ekk86OV9DH0jQJnO9c0pPzHYCHRV04NDbniU4STgZPc3S24o58NR1-ZOoGSqGTN-XxMZ6eVu9iHXc_3nYfU5KDpd4qdsNQDpZmvEIpeXkRLpG3w6CN7z-cnDPt4tBmJ6myghdkhMdU5u-m-MEZ_WySf8mNDi7ncPe_NnsdrsUIkx2sIbEHF3wzgd2xewOLyjyBq1tUhPT0dsPf2k9gL47q2ePIS_3kBszJILLPbTf7Rkhls4b1gZLAczp1h__tbKiJ_PqczQmN7OjoBTvTi3C1jgdP6ZijlVYDzTivO-9ZS8bqS6wCZauZZmtuEtYvu64NP_f6m_Dp8NXHl695bNjArUBc8Dp1Gus0SzLvRekwpDiNcbWvvaul1MII9E7WJKG8MpaCRU_hEBpT5uhznYlbsNO0jb8NTFrjUktQkU7klUWUWufGVEKXOtNGTiEZJadsZDMPTTXO1DkPcxCBIhGoIAJVTuHp5pP5msrjb4MfBTiooOY0r9WxWoF2Fwiz1EFJxg7p9JlMYX9EjIr63yuCuZAi1B1P4cHmNWluSMfoxrdLGlNQeFhUSUmLPRtRtDXFn7Z2559G34Ur2dDBI9zR3IedRbf09-CyXS1mfXd_UJ3v-7ITrg priority: 102 providerName: Springer Nature
Title	New horizons in sphere-packing theory, part II: lattice-based derivative-free optimization via global surrogates
URI	https://link.springer.com/article/10.1007/s10898-012-9866-7 https://www.proquest.com/docview/1323632043 https://www.proquest.com/docview/1506359077
Volume	56
WOSCitedRecordID	wos000317079100004&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: 1573-2916 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0009852 issn: 0925-5001 databaseCode: 7WY dateStart: 19970101 isFulltext: true titleUrlDefault: https://www.proquest.com/abicomplete providerName: ProQuest – providerCode: PRVPQU databaseName: ABI/INFORM Global customDbUrl: eissn: 1573-2916 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0009852 issn: 0925-5001 databaseCode: M0C dateStart: 19970101 isFulltext: true titleUrlDefault: https://search.proquest.com/abiglobal providerName: ProQuest – providerCode: PRVPQU databaseName: Advanced Technologies & Aerospace Database customDbUrl: eissn: 1573-2916 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0009852 issn: 0925-5001 databaseCode: P5Z dateStart: 19970101 isFulltext: true titleUrlDefault: https://search.proquest.com/hightechjournals providerName: ProQuest – providerCode: PRVPQU databaseName: Computer Science Database customDbUrl: eissn: 1573-2916 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0009852 issn: 0925-5001 databaseCode: K7- dateStart: 19970101 isFulltext: true titleUrlDefault: http://search.proquest.com/compscijour providerName: ProQuest – providerCode: PRVPQU databaseName: Engineering Database customDbUrl: eissn: 1573-2916 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0009852 issn: 0925-5001 databaseCode: M7S dateStart: 19970101 isFulltext: true titleUrlDefault: http://search.proquest.com providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 1573-2916 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0009852 issn: 0925-5001 databaseCode: BENPR dateStart: 19970101 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVPQU databaseName: Research Library customDbUrl: eissn: 1573-2916 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0009852 issn: 0925-5001 databaseCode: M2O dateStart: 19970101 isFulltext: true titleUrlDefault: https://search.proquest.com/pqrl providerName: ProQuest – providerCode: PRVPQU databaseName: Science Database customDbUrl: eissn: 1573-2916 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0009852 issn: 0925-5001 databaseCode: M2P dateStart: 19970101 isFulltext: true titleUrlDefault: https://search.proquest.com/sciencejournals providerName: ProQuest – providerCode: PRVAVX databaseName: SpringerLINK Contemporary 1997-Present customDbUrl: eissn: 1573-2916 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0009852 issn: 0925-5001 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/eLvHCXMwpV1Lb9QwELZoywEOQAuoC2VlJCSeVhMnsR0uqFStqIBl1UJbuER-RaxUNkuyuxL8emayTreA6IXLXBKPLc3L9ni-IeRRVmZOGZuySEcRA4enmXI2Zw5iNRx-ROxaSKHjd3IwUKen-TBcuDXhWWXnE1tH7SqLd-TbMDARCVZyvpp8Z9g1CrOroYXGClmLOY9Rz99KtgTdVW3HnSjnGcvAH3dZzUXpnMLispizXAnB5G9x6U_v_FeatI0--zf_d923yI2w76Q7C0VZJ1f8eINcv4BGuEHWg5039EkAo356m0zAC9KvwPAnqCcdjWmDOASewVEbL9lpWwj54wWdgArSg4OX9ExP8T0dw_DoqAPe8xZbnJW197QCD_UtlH7S-UjTBSAJbWZ1XeGNXnOHfNrf-7j7hoUuDcwmSk1ZGTutyphH3PtEOoV5TWNc6UvvSiF0YhLlnShBFmluLOwQPeyBlDEyVT7VPLlLVsfV2G8SKqxxsQX9EC5Jc6uU0Do1Jk-01Fwb0SNRJ6PCBghz7KRxVizBl1GsBYi1QLEWskeenQ-ZLPA7Lvv5MQq-QNsGvlaHEgVYHaJkFTsSPJyCI2fUI1udtItg9E2xFHWPPDz_DOaKORg99tUM_slgT5jlkYTJnnc6dYHFv5Z27_IJ75NrvO3TgS8xt8jqtJ75B-SqnU9HTd0nK_Lkc5-svd4bDA_7rY0AfR_tIuUfWjpEKo-ADrMvQA-Pjn8BSs8bKQ
linkProvider	ProQuest
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3JbtRAEC1FAQk4AAmgDARoJBBbWni8tNtICEWBKKMMIw4hys30ZjFSsI09Myh8FN9IlZdMAJFbDpxtt7dXr7q6ul4BPI6yyEptQu4pz-NIeIpLaxJu0Vdj8COGtpEUOhzHk4k8Oko-rsDPvhaGtlX2nNgQtS0MrZG_wgsDEVAl59vyG6euUZRd7VtotLDYdyffMWSr34ze4f994vu77w929njXVYCbQMoZz4ZWyWyIQb9zQWwl5eG0tpnLnM2EUIEOpLMikxFGJtrgjMahz5Zax6F0oSKhA6T8S2GI5kBbBb2dpcivbDr8eIkf8Qj5v8-itqV6korZhj5PpBA8_s0P_ukN_krLNt5u98b_9p1uwvVuXs22W0NYgxWXr8O1M2qL67DW8VjNnnVi289vQYksz77gC_xA82PTnNWks-B4qQwlEVhT6HmyxUo0MTYavWbHakb7BTm5f8ssjr1otNN5VjnHCmTgr11pK1tMFWsFV1g9r6qCVizr2_DpQr7DHVjNi9xtABNG26FB_AsbhImRUigVap0EKla-0mIAXo-J1HQS7dQp5DhdiksTjFKEUUowSuMBvDi9pGz1Sc47-SkBLSXuwnGN6kow8OlIBSzdjpHBJYbU3gA2e3SlHanV6RJaA3h0ehjpiHJMKnfFHM-JcM4bJV6MN3vZY_jMEP96tLvn3_AhXNk7-DBOx6PJ_j246jc9SWjX6Saszqq5uw-XzWI2rasHjUUy-HzR0P4FOr5x_w
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Lb9NAEB5VBSE4AC0gAgUWCcRzVT_XaySEKkpE1CrKAVDVi9mXRaRimzgJKj-NX8eMH00B0VsPnG2vX998s7Oz8w3AoziPrdQm4p7yPI6Ep7i0JuUWfTUGP8K3jaTQp_1kPJYHB-lkDX72tTC0rbLnxIaobWlojXwbLwxFSJWc23m3LWKyO3xTfePUQYoyrX07jRYie-74O4Zv9evRLv7rx0EwfPfh7XvedRjgJpRyznPfKpn7gRc4FyZWUk5Oa5u73NlcCBXqUDorchljlKINzm4c-m-pdRJJFykSPUD6v5BgjEmB3yQ-XAn-yqbbj5cGMY_RF_QZ1bZsT1Jhmx_wVArBk9984p-e4a8UbeP5htf-5292Ha5282220xrIBqy5YhOunFJh3ISNjt9q9rQT4X52Aypkf_YFX-AHmiWbFqwm_QXHK2UoucCaAtDjl6xC02Oj0St2pOa0j5DTtMAyi2MvG011ns-cYyUy89eu5JUtp4q1QiysXsxmJa1k1jfh47l8h1uwXpSFuw1MGG19g3YhbBilRkqhVKR1GqpEBUqLAXg9PjLTSbdTB5GjbCU6TZDKEFIZQSpLBvD85JKq1S056-QnBLqMOA3HNaorzcCnI3WwbCdBZpcYansD2OqRlnVkV2crmA3g4clhpCnKPanClQs8J8a5cJx6Cd7sRY_nU0P869HunH3DB3AJEZ3tj8Z7d-Fy0LQqoc2oW7A-ny3cPbholvNpPbvfGCeDz-eN7F9DUXsQ
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=New+horizons+in+sphere-packing+theory%2C+part+II%3A+lattice-based+derivative-free+optimization+via+global+surrogates&rft.jtitle=Journal+of+global+optimization&rft.au=Belitz%2C+Paul&rft.au=Bewley%2C+Thomas&rft.date=2013-05-01&rft.pub=Springer+Nature+B.V&rft.issn=0925-5001&rft.eissn=1573-2916&rft.volume=56&rft.issue=1&rft.spage=61&rft_id=info:doi/10.1007%2Fs10898-012-9866-7&rft.externalDBID=HAS_PDF_LINK&rft.externalDocID=2936184251
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0925-5001&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0925-5001&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0925-5001&client=summon