Derivative-free methods for mixed-integer nonsmooth constrained optimization
In this paper, mixed-integer nonsmooth constrained optimization problems are considered, where objective/constraint functions are available only as the output of a black-box zeroth-order oracle that does not provide derivative information. A new derivative-free linesearch-based algorithmic framework...
Gespeichert in:
| Veröffentlicht in: | Computational optimization and applications Jg. 82; H. 2; S. 293 - 327 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
New York
Springer US
01.06.2022
Springer Nature B.V |
| Schlagworte: | |
| ISSN: | 0926-6003, 1573-2894 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | In this paper, mixed-integer nonsmooth constrained optimization problems are considered, where objective/constraint functions are available only as the output of a black-box zeroth-order oracle that does not provide derivative information. A new derivative-free linesearch-based algorithmic framework is proposed to suitably handle those problems. First, a scheme for bound constrained problems that combines a dense sequence of directions to handle the nonsmoothness of the objective function with primitive directions to handle discrete variables is described. Then, an exact penalty approach is embedded in the scheme to suitably manage nonlinear (possibly nonsmooth) constraints. Global convergence properties of the proposed algorithms toward stationary points are analyzed and results of an extensive numerical experience on a set of mixed-integer test problems are reported. |
|---|---|
| AbstractList | In this paper, mixed-integer nonsmooth constrained optimization problems are considered, where objective/constraint functions are available only as the output of a black-box zeroth-order oracle that does not provide derivative information. A new derivative-free linesearch-based algorithmic framework is proposed to suitably handle those problems. First, a scheme for bound constrained problems that combines a dense sequence of directions to handle the nonsmoothness of the objective function with primitive directions to handle discrete variables is described. Then, an exact penalty approach is embedded in the scheme to suitably manage nonlinear (possibly nonsmooth) constraints. Global convergence properties of the proposed algorithms toward stationary points are analyzed and results of an extensive numerical experience on a set of mixed-integer test problems are reported. |
| Author | Giovannelli, Tommaso Rinaldi, Francesco Lucidi, Stefano Liuzzi, Giampaolo |
| Author_xml | – sequence: 1 givenname: Tommaso surname: Giovannelli fullname: Giovannelli, Tommaso organization: Department of Industrial and Systems Engineering, Lehigh University – sequence: 2 givenname: Giampaolo orcidid: 0000-0002-4063-8370 surname: Liuzzi fullname: Liuzzi, Giampaolo email: liuzzi@diag.uniroma1.it organization: Dipartimento di Ingegneria Informatica, Automatica e Gestionale, Sapienza Università di Roma and Istituto di Analisi dei Sistemi e Informatica (IASI), CNR – sequence: 3 givenname: Stefano surname: Lucidi fullname: Lucidi, Stefano organization: Dipartimento di Ingegneria Informatica, Automatica e Gestionale, Sapienza Università di Roma – sequence: 4 givenname: Francesco surname: Rinaldi fullname: Rinaldi, Francesco organization: Dipartimento di Matematica “Tullio Levi-Civita”, Università di Padova |
| BookMark | eNp9kE1LAzEURYNUsK3-AVcDrqP5mJk0S6mfUHCj65DJvNiUzqQmaVF_vWlHEFx0lQe5573LmaBR73tA6JKSa0qIuImUVDOJCWOYEF5zTE_QmFaCYzaT5QiNiWQ1rvPfGZrEuCKESMHZGC3uILidTm4H2AaAooO09G0srA9F5z6hxa5P8A6hyCdj531aFiZPKWjXQ1v4TXKd-84bfH-OTq1eR7j4fafo7eH-df6EFy-Pz_PbBTa5WsJU2xIq2tqWQAWUlxJKrmkLwlLGStOA0VIa0bRCczEjstKG2YbwRlDDGOdTdDXs3QT_sYWY1MpvQ59PKlbXtaBUUJlTsyFlgo8xgFXGpUPPffe1okTt3anBncru1MGdohll_9BNcJ0OX8chPkAxh_ts7K_VEeoHcGGE6A |
| CitedBy_id | crossref_primary_10_1007_s10729_024_09678_3 crossref_primary_10_1109_JIOT_2025_3531932 crossref_primary_10_1007_s10898_024_01426_9 crossref_primary_10_3390_math11132920 crossref_primary_10_1016_j_matcom_2023_10_021 crossref_primary_10_1109_JIOT_2025_3538508 crossref_primary_10_1007_s12532_025_00281_3 |
| Cites_doi | 10.1016/0041-5553(76)90154-3 10.1093/imanum/drn045 10.1007/s10898-013-0101-y 10.1007/s10589-014-9660-1 10.1007/s11081-015-9281-2 10.1137/1.9780898718768 10.1137/050646706 10.1137/130940037 10.1007/s10957-014-0617-4 10.1007/s12532-020-00182-7 10.1007/978-3-319-68913-5 10.1017/s0962492919000060 10.1137/S1052623403429573 10.1137/S1052623493250780 10.1137/S1052623499352024 10.1007/s11590-008-0089-2 10.1016/j.cor.2012.08.022 10.1145/3085592 10.1137/080724083 10.1007/s11081-011-9168-9 10.1137/S105262340138983X 10.1007/BF01189901 10.1007/s10589-011-9405-3 10.1007/s12532-018-0144-7 10.1007/s12065-019-00326-2 10.1016/j.ejor.2015.12.018 10.1007/s10898-020-00978-w 10.1137/070692662 10.1007/s10107-010-0429-8 10.1007/s11081-008-9048-0 10.1145/42288.214372 10.1515/9781400873173 10.1137/18M1175872 10.1137/S1052623497330392 10.1016/0022-247X(67)90163-1 10.1016/j.ejor.2008.10.020 10.1137/040603371 10.1007/BF01584534 10.1007/BF01386213 10.1137/S1052623400370606 10.1137/080716980 10.1007/s10589-009-9266-1 10.1145/1916461.1916468 10.1007/s101070100263 |
| ContentType | Journal Article |
| Copyright | The Author(s) 2022. corrected publication 2022 The Author(s) 2022. corrected publication 2022. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| Copyright_xml | – notice: The Author(s) 2022. corrected publication 2022 – notice: The Author(s) 2022. corrected publication 2022. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| DBID | C6C AAYXX CITATION 3V. 7SC 7WY 7WZ 7XB 87Z 88I 8AL 8AO 8FD 8FE 8FG 8FK 8FL ABJCF ABUWG AFKRA ARAPS AZQEC BENPR BEZIV BGLVJ CCPQU DWQXO FRNLG F~G GNUQQ HCIFZ JQ2 K60 K6~ K7- L.- L6V L7M L~C L~D M0C M0N M2P M7S P5Z P62 PHGZM PHGZT PKEHL PQBIZ PQBZA PQEST PQGLB PQQKQ PQUKI PRINS PTHSS Q9U |
| DOI | 10.1007/s10589-022-00363-1 |
| DatabaseName | Springer Nature OA Free Journals CrossRef ProQuest Central (Corporate) Computer and Information Systems Abstracts ABI/INFORM Collection ABI/INFORM Global (PDF only) ProQuest Central (purchase pre-March 2016) ABI/INFORM Collection Science Database (Alumni Edition) Computing Database (Alumni Edition) ProQuest Pharma Collection Technology Research Database ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central (Alumni) (purchase pre-March 2016) ABI/INFORM Collection (Alumni Edition) Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection ProQuest Central Essentials ProQuest Central Business Premium Collection Technology collection ProQuest One Community College ProQuest Central Business Premium Collection (Alumni) ABI/INFORM Global (Corporate) ProQuest Central Student SciTech Premium Collection ProQuest Computer Science Collection ProQuest Business Collection (Alumni Edition) ProQuest Business Collection Computer Science Database ABI/INFORM Professional Advanced ProQuest Engineering Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional ABI/INFORM Global Computing Database Science Database (subscription) 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 | ProQuest Business Collection (Alumni Edition) CrossRef |
| Database_xml | – sequence: 1 dbid: BENPR name: ProQuest Central url: https://www.proquest.com/central sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Statistics Mathematics |
| EISSN | 1573-2894 |
| EndPage | 327 |
| ExternalDocumentID | 10_1007_s10589_022_00363_1 |
| GroupedDBID | -52 -5D -5G -BR -EM -Y2 -~C .4S .86 .DC .VR 06D 0R~ 0VY 1N0 1SB 2.D 203 28- 29F 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2~H 30V 3V. 4.4 406 408 409 40D 40E 5GY 5QI 5VS 67Z 6NX 7WY 88I 8AO 8FE 8FG 8FL 8FW 8TC 8UJ 8VB 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDZT ABECU ABFTV ABHLI ABHQN ABJCF ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABUWG ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACGOD ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSNA ACZOJ ADHHG ADHIR ADINQ ADKNI ADKPE ADMLS ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFEXP AFGCZ AFKRA AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHQJS AHSBF AHYZX AI. AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ AKVCP ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARAPS ARCSS ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN AZQEC B-. BA0 BAPOH BBWZM BDATZ BENPR BEZIV BGLVJ BGNMA BPHCQ BSONS C6C CAG CCPQU COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP DU5 DWQXO EBLON EBS EBU EDO EIOEI EJD ESBYG F5P FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRNLG FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNUQQ GNWQR GQ6 GQ7 GQ8 GROUPED_ABI_INFORM_COMPLETE GROUPED_ABI_INFORM_RESEARCH GXS H13 HCIFZ HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I-F I09 IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ K1G K60 K6V K6~ K7- KDC KOV KOW L6V LAK LLZTM M0C M0N M2P M4Y M7S MA- N2Q N9A NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM OVD P19 P2P P62 P9R PF0 PQBIZ PQBZA PQQKQ PROAC PT4 PT5 PTHSS Q2X QOK QOS QWB R4E R89 R9I RHV RNI RNS ROL RPX RSV RZC RZD RZK S16 S1Z S26 S27 S28 S3B SAP SCLPG SDD SDH SDM SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TEORI TH9 TN5 TSG TSK TSV TUC TUS U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW VH1 W23 W48 WK8 YLTOR Z45 Z7R Z7S Z7X Z81 Z83 Z86 Z88 Z8M Z8N Z8R Z8U Z8W Z92 ZL0 ZMTXR ZWQNP ~8M ~EX AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC ADHKG AEZWR AFDZB AFFHD AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP AMVHM ATHPR AYFIA CITATION PHGZM PHGZT PQGLB 7SC 7XB 8AL 8FD 8FK JQ2 L.- L7M L~C L~D PKEHL PQEST PQUKI PRINS Q9U |
| ID | FETCH-LOGICAL-c363t-1af4e51dfd0e5e1349e43a1de7f1224cbeca99c7bd7a378095ac2fb03b71c2233 |
| IEDL.DBID | BENPR |
| ISICitedReferencesCount | 10 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000777251900001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0926-6003 |
| IngestDate | Wed Nov 26 14:53:03 EST 2025 Sat Nov 29 01:51:30 EST 2025 Tue Nov 18 20:12:49 EST 2025 Fri Feb 21 02:44:58 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 2 |
| Keywords | Nonsmooth optimization 65K05 Mixed-integer nonlinear programming 90C11 90C56 Derivative-free optimization |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c363t-1af4e51dfd0e5e1349e43a1de7f1224cbeca99c7bd7a378095ac2fb03b71c2233 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0002-4063-8370 |
| OpenAccessLink | https://link.springer.com/10.1007/s10589-022-00363-1 |
| PQID | 2666711719 |
| PQPubID | 30811 |
| PageCount | 35 |
| ParticipantIDs | proquest_journals_2666711719 crossref_citationtrail_10_1007_s10589_022_00363_1 crossref_primary_10_1007_s10589_022_00363_1 springer_journals_10_1007_s10589_022_00363_1 |
| PublicationCentury | 2000 |
| PublicationDate | 20220600 2022-06-00 20220601 |
| PublicationDateYYYYMMDD | 2022-06-01 |
| PublicationDate_xml | – month: 6 year: 2022 text: 20220600 |
| PublicationDecade | 2020 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York |
| PublicationSubtitle | An International Journal |
| PublicationTitle | Computational optimization and applications |
| PublicationTitleAbbrev | Comput Optim Appl |
| PublicationYear | 2022 |
| Publisher | Springer US Springer Nature B.V |
| Publisher_xml | – name: Springer US – name: Springer Nature B.V |
| References | Torczon (CR50) 1997; 7 CR38 Moré, Wild (CR40) 2009; 20 Newby, Ali (CR44) 2014; 60 Audet, Le Digabel, Tribes (CR11) 2019; 29 Clarke (CR14) 1983 Bratley, Fox (CR13) 1988; 14 Mangasarian, Fromovitz (CR39) 1967; 17 Vicente, Custódio (CR51) 2009; 133 Garcìa-Palomares, Rodriguez (CR22) 2002; 13 Larson, Menickelly, Wild (CR30) 2019; 28 Müller, Shoemaker, Piché (CR43) 2013; 40 Di Pillo, Facchinei (CR19) 1995; 32 Jahn (CR28) 2014 Larson, Leyffer, Palkar, Wild (CR31) 2021; 1 Audet, Dennis (CR5) 2004 Garcìa-Palomares, Costa-Montenegro, Asorey Cacheda, González-Castaño (CR23) 2012 CR9 CR46 Sobol (CR48) 1976; 16 Audet, Hare (CR8) 2017 Boukouvala, Misener, Floudas (CR12) 2015 Dolan, Moré (CR20) 2002; 91 Conn, Scheinberg, Vicente (CR15) 2009 Abramson, Audet, Chrissis, Walston (CR2) 2009; 3 Müller, Shoemaker, Piché (CR42) 2013 Gould, Tolle (CR24) 1972 Porcelli, Toint (CR45) 2017; 44 Le Digabel (CR32) 2011; 37 Liuzzi, Lucidi, Rinaldi (CR34) 2014 Abramson, Audet (CR1) 2004; 3 Rockafellar (CR47) 1970 Audet, Dennis (CR4) 2001 Halton (CR26) 1960; 2 Hemker, Fowler, Farthing, Von Stryk (CR27) 2008; 9 Lucidi, Sciandrone (CR36) 2002; 13 Audet, Dennis, Le Digabel (CR10) 2010; 46 Costa, Nannicini (CR16) 2018; 10 Audet, Dennis (CR7) 2009; 20 Custódio, Vicente (CR17) 2007; 18 Custódio, Dennis, Vicente (CR18) 2008; 28 Liuzzi, Lucidi, Rinaldi (CR33) 2012 Abramson, Audet, Dennis, Le Digabel (CR3) 2009; 20 Audet, Dennis (CR6) 2006; 17 CR29 Lucidi, Piccialli, Sciandrone (CR37) 2005 CR25 Liuzzi, Lucidi, Rinaldi (CR35) 2020; 12 Müller (CR41) 2015; 17 Sriver, Chrissis, Abramson (CR49) 2009; 198 Fasano, Liuzzi, Lucidi, Rinaldi (CR21) 2014; 24 Yang, Liu, Pan (CR52) 2019 S Lucidi (363_CR36) 2002; 13 363_CR38 AL Custódio (363_CR18) 2008; 28 ED Dolan (363_CR20) 2002; 91 J Jahn (363_CR28) 2014 V Torczon (363_CR50) 1997; 7 AL Custódio (363_CR17) 2007; 18 C Audet (363_CR7) 2009; 20 C Audet (363_CR10) 2010; 46 RT Rockafellar (363_CR47) 1970 UM Garcìa-Palomares (363_CR22) 2002; 13 JH Halton (363_CR26) 1960; 2 363_CR46 J Larson (363_CR31) 2021; 1 FJ Gould (363_CR24) 1972 F Clarke (363_CR14) 1983 G Liuzzi (363_CR34) 2014 J Larson (363_CR30) 2019; 28 TA Sriver (363_CR49) 2009; 198 M Abramson (363_CR1) 2004; 3 C Audet (363_CR6) 2006; 17 S Yang (363_CR52) 2019 O Mangasarian (363_CR39) 1967; 17 P Bratley (363_CR13) 1988; 14 C Audet (363_CR4) 2001 A Costa (363_CR16) 2018; 10 I Sobol (363_CR48) 1976; 16 G Liuzzi (363_CR33) 2012 C Audet (363_CR11) 2019; 29 G Fasano (363_CR21) 2014; 24 UM Garcìa-Palomares (363_CR23) 2012 G Di Pillo (363_CR19) 1995; 32 E Newby (363_CR44) 2014; 60 M Porcelli (363_CR45) 2017; 44 LN Vicente (363_CR51) 2009; 133 J Müller (363_CR43) 2013; 40 T Hemker (363_CR27) 2008; 9 J Müller (363_CR42) 2013 363_CR9 363_CR29 M Abramson (363_CR3) 2009; 20 F Boukouvala (363_CR12) 2015 363_CR25 C Audet (363_CR5) 2004 G Liuzzi (363_CR35) 2020; 12 S Lucidi (363_CR37) 2005 C Audet (363_CR8) 2017 J Müller (363_CR41) 2015; 17 M Abramson (363_CR2) 2009; 3 S Le Digabel (363_CR32) 2011; 37 A Conn (363_CR15) 2009 J Moré (363_CR40) 2009; 20 |
| References_xml | – volume: 16 start-page: 236 issue: 5 year: 1976 end-page: 242 ident: CR48 article-title: Uniformly distributed sequences with an additional uniform property publication-title: USSR Comput. Math. Math. Phys. doi: 10.1016/0041-5553(76)90154-3 – volume: 28 start-page: 770 issue: 4 year: 2008 end-page: 784 ident: CR18 article-title: Using simplex gradients of nonsmooth functions in direct search methods publication-title: IMA J. Numer. Anal. doi: 10.1093/imanum/drn045 – year: 2013 ident: CR42 article-title: SO-I: A surrogate model algorithm for expensive nonlinear integer programming problems including global optimization applications publication-title: J. Glob. Optim. doi: 10.1007/s10898-013-0101-y – volume: 3 start-page: 1 year: 2004 end-page: 10 ident: CR1 article-title: Filter pattern search algorithms for mixed variable constrained optimization problems publication-title: Pac. J. Optim. – volume: 60 start-page: 199 year: 2014 end-page: 229 ident: CR44 article-title: A trust-region-based derivative free algorithm for mixed integer programming publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-014-9660-1 – volume: 17 start-page: 1 year: 2015 end-page: 27 ident: CR41 article-title: MISO: mixed-integer surrogate optimization framework publication-title: Optim. Eng. doi: 10.1007/s11081-015-9281-2 – year: 2009 ident: CR15 publication-title: Introduction to Derivative-Free Optimization doi: 10.1137/1.9780898718768 – volume: 18 start-page: 537 year: 2007 end-page: 555 ident: CR17 article-title: Using sampling and simplex derivatives in pattern search methods publication-title: SIAM J. Optim. doi: 10.1137/050646706 – volume: 24 start-page: 959 year: 2014 end-page: 992 ident: CR21 article-title: A linesearch-based derivative-free approach for nonsmooth constrained optimization publication-title: SIAM J. Optim. doi: 10.1137/130940037 – ident: CR29 – year: 2014 ident: CR34 article-title: Derivative-free methods for mixed-integer constrained optimization problems publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-014-0617-4 – volume: 12 start-page: 673 year: 2020 end-page: 702 ident: CR35 article-title: An algorithmic framework based on primitive directions and nonmonotone line searches for black-box optimization problems with integer variables publication-title: Math. Program. Comput. doi: 10.1007/s12532-020-00182-7 – year: 2017 ident: CR8 publication-title: Derivative-Free and Blackbox Optimization doi: 10.1007/978-3-319-68913-5 – ident: CR25 – volume: 28 start-page: 287 year: 2019 end-page: 404 ident: CR30 article-title: Derivative-free optimization methods publication-title: Acta Num. doi: 10.1017/s0962492919000060 – year: 2005 ident: CR37 article-title: An algorithm model for mixed variable programming publication-title: SIAM J. Optim. doi: 10.1137/S1052623403429573 – ident: CR46 – volume: 7 start-page: 1 issue: 1 year: 1997 end-page: 25 ident: CR50 article-title: On the convergence of pattern search algorithms publication-title: SIAM J. Optim. doi: 10.1137/S1052623493250780 – year: 2001 ident: CR4 article-title: Pattern search algorithms for mixed variable programming publication-title: SIAM J. Optim. doi: 10.1137/S1052623499352024 – volume: 3 start-page: 35 year: 2009 end-page: 47 ident: CR2 article-title: Mesh adaptive direct search algorithms for mixed variable optimization publication-title: Optim. Lett. doi: 10.1007/s11590-008-0089-2 – volume: 40 start-page: 1383 issue: 5 year: 2013 end-page: 1400 ident: CR43 article-title: SO-MI: A surrogate model algorithm for computationally expensive nonlinear mixed-integer black-box global optimization problems publication-title: Comput. Oper. Res. doi: 10.1016/j.cor.2012.08.022 – volume: 44 start-page: 1 year: 2017 end-page: 25 ident: CR45 article-title: BFO, a trainable derivative-free brute force optimizer for nonlinear bound-constrained optimization and equilibrium computations with continuous and discrete variables publication-title: ACM Trans. Math. Softw. doi: 10.1145/3085592 – year: 1983 ident: CR14 publication-title: Optimization and Nonsmooth Analysis – ident: CR9 – volume: 20 start-page: 172 year: 2009 end-page: 191 ident: CR40 article-title: Benchmarking derivative-free optimization algorithms publication-title: SIAM J. Optim. doi: 10.1137/080724083 – year: 2012 ident: CR23 article-title: Adapting derivative free optimization methods to engineering models with discrete variables publication-title: Optim. Eng. doi: 10.1007/s11081-011-9168-9 – year: 2004 ident: CR5 article-title: A pattern search filter method for nonlinear programming without derivatives publication-title: SIAM J. Optim. doi: 10.1137/S105262340138983X – volume: 32 start-page: 1 issue: 1 year: 1995 end-page: 31 ident: CR19 article-title: Exact barrier function methods for Lipschitz programs publication-title: Appl. Math. Optim. doi: 10.1007/BF01189901 – year: 2012 ident: CR33 article-title: Derivative-free methods for bound constrained mixed-integer optimization publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-011-9405-3 – volume: 10 start-page: 597 year: 2018 end-page: 629 ident: CR16 article-title: RBFOpt: an open-source library for black-box optimization with costly function evaluations publication-title: Math. Program. Comput. doi: 10.1007/s12532-018-0144-7 – year: 2019 ident: CR52 article-title: An efficient derivative-free algorithm for bound constrained mixed-integer optimization publication-title: Evol. Intell. doi: 10.1007/s12065-019-00326-2 – year: 2015 ident: CR12 article-title: Global optimization advances in mixed-integer nonlinear programming, minlp, and constrained derivative-free optimization, cdfo publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2015.12.018 – volume: 1 start-page: 1 year: 2021 end-page: 39 ident: CR31 article-title: A method for convex black-box integer global optimization publication-title: J. Glob. Optim. doi: 10.1007/s10898-020-00978-w – volume: 20 start-page: 445 issue: 1 year: 2009 end-page: 472 ident: CR7 article-title: A progressive barrier for derivative-free nonlinear programming publication-title: SIAM J. Optim. doi: 10.1137/070692662 – volume: 133 start-page: 1 year: 2009 end-page: 27 ident: CR51 article-title: Analysis of direct searches for discontinuous functions publication-title: Math. Program. doi: 10.1007/s10107-010-0429-8 – volume: 9 start-page: 341 year: 2008 end-page: 360 ident: CR27 article-title: A mixed-integer simulation-based optimization approach with surrogate functions in water resources management publication-title: Optim. Eng. doi: 10.1007/s11081-008-9048-0 – volume: 14 start-page: 88 issue: 1 year: 1988 end-page: 100 ident: CR13 article-title: Algorithm 659: implementing Sobol’s quasirandom sequence generator publication-title: ACM Trans. Math. Softw. doi: 10.1145/42288.214372 – year: 1970 ident: CR47 publication-title: Convex Analysis doi: 10.1515/9781400873173 – volume: 29 start-page: 1164 year: 2019 end-page: 1189 ident: CR11 article-title: The mesh adaptive direct search algorithm for granular and discrete variables publication-title: SIAM J. Optim. doi: 10.1137/18M1175872 – volume: 13 start-page: 97 year: 2002 end-page: 116 ident: CR36 article-title: On the global convergence of derivative-free methods for unconstrained optimization publication-title: SIAM J. Optim. doi: 10.1137/S1052623497330392 – year: 2014 ident: CR28 publication-title: Introduction to the Theory of Nonlinear Optimization – volume: 17 start-page: 37 issue: 1 year: 1967 end-page: 47 ident: CR39 article-title: The fritz john necessary optimality conditions in the presence of equality and inequality constraints publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(67)90163-1 – volume: 198 start-page: 878 issue: 3 year: 2009 end-page: 890 ident: CR49 article-title: Pattern search ranking and selection algorithms for mixed variable simulation-based optimization publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2008.10.020 – volume: 17 start-page: 188 year: 2006 end-page: 217 ident: CR6 article-title: Mesh adaptive direct search algorithms for constrained optimization publication-title: SIAM J. Optim. doi: 10.1137/040603371 – volume: 91 start-page: 201 issue: 2 year: 2002 end-page: 213 ident: CR20 article-title: Benchmarking optimization software with performance profiles publication-title: Math. Program. – year: 1972 ident: CR24 article-title: Geometry of optimality conditions and constraint qualifications publication-title: Math. Program. doi: 10.1007/BF01584534 – volume: 2 start-page: 84 issue: 1 year: 1960 end-page: 90 ident: CR26 article-title: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals publication-title: Num. Math. doi: 10.1007/BF01386213 – ident: CR38 – volume: 13 start-page: 79 year: 2002 end-page: 96 ident: CR22 article-title: New sequential and parallel derivative-free algorithms for unconstrained minimization publication-title: SIAM J. Optim. doi: 10.1137/S1052623400370606 – volume: 20 start-page: 948 year: 2009 end-page: 966 ident: CR3 article-title: OrthoMADS: a deterministic MADS instance with orthogonal directions publication-title: SIAM J. Optim. doi: 10.1137/080716980 – volume: 46 start-page: 193 year: 2010 end-page: 215 ident: CR10 article-title: Globalization strategies for mesh adaptive direct search publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-009-9266-1 – volume: 37 start-page: 1 issue: 4 year: 2011 end-page: 15 ident: CR32 article-title: Algorithm 909: NOMAD: Nonlinear optimization with the MADS algorithm publication-title: ACM Trans. Math. Softw. doi: 10.1145/1916461.1916468 – year: 2012 ident: 363_CR23 publication-title: Optim. Eng. doi: 10.1007/s11081-011-9168-9 – volume: 24 start-page: 959 year: 2014 ident: 363_CR21 publication-title: SIAM J. Optim. doi: 10.1137/130940037 – volume: 20 start-page: 948 year: 2009 ident: 363_CR3 publication-title: SIAM J. Optim. doi: 10.1137/080716980 – volume: 17 start-page: 188 year: 2006 ident: 363_CR6 publication-title: SIAM J. Optim. doi: 10.1137/040603371 – volume: 37 start-page: 1 issue: 4 year: 2011 ident: 363_CR32 publication-title: ACM Trans. Math. Softw. doi: 10.1145/1916461.1916468 – volume: 1 start-page: 1 year: 2021 ident: 363_CR31 publication-title: J. Glob. Optim. doi: 10.1007/s10898-020-00978-w – volume: 18 start-page: 537 year: 2007 ident: 363_CR17 publication-title: SIAM J. Optim. doi: 10.1137/050646706 – volume: 32 start-page: 1 issue: 1 year: 1995 ident: 363_CR19 publication-title: Appl. Math. Optim. doi: 10.1007/BF01189901 – year: 2019 ident: 363_CR52 publication-title: Evol. Intell. doi: 10.1007/s12065-019-00326-2 – volume-title: Convex Analysis year: 1970 ident: 363_CR47 doi: 10.1515/9781400873173 – volume: 60 start-page: 199 year: 2014 ident: 363_CR44 publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-014-9660-1 – volume: 3 start-page: 1 year: 2004 ident: 363_CR1 publication-title: Pac. J. Optim. – volume: 17 start-page: 1 year: 2015 ident: 363_CR41 publication-title: Optim. Eng. doi: 10.1007/s11081-015-9281-2 – year: 1972 ident: 363_CR24 publication-title: Math. Program. doi: 10.1007/BF01584534 – year: 2015 ident: 363_CR12 publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2015.12.018 – year: 2001 ident: 363_CR4 publication-title: SIAM J. Optim. doi: 10.1137/S1052623499352024 – ident: 363_CR38 – volume: 17 start-page: 37 issue: 1 year: 1967 ident: 363_CR39 publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(67)90163-1 – volume: 13 start-page: 97 year: 2002 ident: 363_CR36 publication-title: SIAM J. Optim. doi: 10.1137/S1052623497330392 – volume: 16 start-page: 236 issue: 5 year: 1976 ident: 363_CR48 publication-title: USSR Comput. Math. Math. Phys. doi: 10.1016/0041-5553(76)90154-3 – volume: 44 start-page: 1 year: 2017 ident: 363_CR45 publication-title: ACM Trans. Math. Softw. doi: 10.1145/3085592 – volume: 28 start-page: 287 year: 2019 ident: 363_CR30 publication-title: Acta Num. doi: 10.1017/s0962492919000060 – volume: 198 start-page: 878 issue: 3 year: 2009 ident: 363_CR49 publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2008.10.020 – year: 2014 ident: 363_CR34 publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-014-0617-4 – volume: 9 start-page: 341 year: 2008 ident: 363_CR27 publication-title: Optim. Eng. doi: 10.1007/s11081-008-9048-0 – volume: 12 start-page: 673 year: 2020 ident: 363_CR35 publication-title: Math. Program. Comput. doi: 10.1007/s12532-020-00182-7 – volume: 91 start-page: 201 issue: 2 year: 2002 ident: 363_CR20 publication-title: Math. Program. doi: 10.1007/s101070100263 – year: 2005 ident: 363_CR37 publication-title: SIAM J. Optim. doi: 10.1137/S1052623403429573 – year: 2013 ident: 363_CR42 publication-title: J. Glob. Optim. doi: 10.1007/s10898-013-0101-y – volume: 28 start-page: 770 issue: 4 year: 2008 ident: 363_CR18 publication-title: IMA J. Numer. Anal. doi: 10.1093/imanum/drn045 – ident: 363_CR9 – volume: 7 start-page: 1 issue: 1 year: 1997 ident: 363_CR50 publication-title: SIAM J. Optim. doi: 10.1137/S1052623493250780 – volume: 46 start-page: 193 year: 2010 ident: 363_CR10 publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-009-9266-1 – volume-title: Optimization and Nonsmooth Analysis year: 1983 ident: 363_CR14 – volume: 20 start-page: 445 issue: 1 year: 2009 ident: 363_CR7 publication-title: SIAM J. Optim. doi: 10.1137/070692662 – volume: 14 start-page: 88 issue: 1 year: 1988 ident: 363_CR13 publication-title: ACM Trans. Math. Softw. doi: 10.1145/42288.214372 – year: 2012 ident: 363_CR33 publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-011-9405-3 – volume: 133 start-page: 1 year: 2009 ident: 363_CR51 publication-title: Math. Program. doi: 10.1007/s10107-010-0429-8 – volume: 10 start-page: 597 year: 2018 ident: 363_CR16 publication-title: Math. Program. Comput. doi: 10.1007/s12532-018-0144-7 – volume-title: Introduction to the Theory of Nonlinear Optimization year: 2014 ident: 363_CR28 – ident: 363_CR46 – volume: 2 start-page: 84 issue: 1 year: 1960 ident: 363_CR26 publication-title: Num. Math. doi: 10.1007/BF01386213 – volume: 40 start-page: 1383 issue: 5 year: 2013 ident: 363_CR43 publication-title: Comput. Oper. Res. doi: 10.1016/j.cor.2012.08.022 – year: 2004 ident: 363_CR5 publication-title: SIAM J. Optim. doi: 10.1137/S105262340138983X – volume: 20 start-page: 172 year: 2009 ident: 363_CR40 publication-title: SIAM J. Optim. doi: 10.1137/080724083 – volume: 13 start-page: 79 year: 2002 ident: 363_CR22 publication-title: SIAM J. Optim. doi: 10.1137/S1052623400370606 – volume: 3 start-page: 35 year: 2009 ident: 363_CR2 publication-title: Optim. Lett. doi: 10.1007/s11590-008-0089-2 – volume-title: Derivative-Free and Blackbox Optimization year: 2017 ident: 363_CR8 doi: 10.1007/978-3-319-68913-5 – volume: 29 start-page: 1164 year: 2019 ident: 363_CR11 publication-title: SIAM J. Optim. doi: 10.1137/18M1175872 – ident: 363_CR29 – volume-title: Introduction to Derivative-Free Optimization year: 2009 ident: 363_CR15 doi: 10.1137/1.9780898718768 – ident: 363_CR25 |
| SSID | ssj0009732 |
| Score | 2.3690014 |
| Snippet | In this paper, mixed-integer nonsmooth constrained optimization problems are considered, where objective/constraint functions are available only as the output... |
| SourceID | proquest crossref springer |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 293 |
| SubjectTerms | Algorithms Constraints Convex and Discrete Geometry Derivatives Management Science Mathematics Mathematics and Statistics Mixed integer Operations Research Operations Research/Decision Theory Optimization Statistics Variables |
| SummonAdditionalLinks | – databaseName: Springer Nature - Connect here FIRST to enable access dbid: RSV link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3NS8MwFA8yPcyDH1NxOiUHbxpo-pXmKOrwoEPwg91KmryC4DZZ5_DP9yVt1ykq6LE0TcP7vSa_9OX9HiEnsVJZJGx2ux8CC6UKWJLrjIlIchPIDBmyQ_pGDAbJcCjvqqSwoj7tXock3Uy9lOwW2eM9uHnyXPQR9zyrkVWbsXv0-6dGale4smSe9GOGy3lQpcp838fn5ajhmF_Com616W_-b5xbZKNil_S8dIdtsgLjDllf0hzEq9uFUGvRIW1LNkut5h1yc4lt5k4JnOVTAFqWly4oEls6en4Hw5y6BEzpGJ11NEGUqbYE09aZAEMnOP-MqsTOXfLYv3q4uGZVtQWmcZQzxlUeQsRNbjyIwKoWQhgobkDkNvqmEWwlpRaZESoQCVIzpf0884JMcI0kI9gjLXw57BMag1JJDDIPuQl9MFKHJhIZTg85V570uoTXRk91JUVuR_qSNiLK1ogpGjF1Rkx5l5wunnkthTh-bd2rsUyrj7JIkYvEgnPBZZec1dg1t3_u7eBvzQ9J23fw2381PdKaTd_giKzpOeI5PXbO-gFigeMy priority: 102 providerName: Springer Nature |
| Title | Derivative-free methods for mixed-integer nonsmooth constrained optimization |
| URI | https://link.springer.com/article/10.1007/s10589-022-00363-1 https://www.proquest.com/docview/2666711719 |
| Volume | 82 |
| WOSCitedRecordID | wos000777251900001&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: Springer Nature - Connect here FIRST to enable access customDbUrl: eissn: 1573-2894 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0009732 issn: 0926-6003 databaseCode: RSV dateStart: 19970101 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LT8MwDLZ4HeDAGzFe6oEbRDR9ZTkhnkICpok3XKo0caVJjME2ED8fJ8soIMGFi9WqbZr2c2M3jj8DbGZKFamw2e1RgiyRKmb1UhdMpJKbWBbkITukz0SjUb-7k00_4dbzyyqHY6IbqE1H2znyHTIkmeBccLn7_MJs1SgbXfUlNEZh3DKVkZ6P7x81mhcV7a5wJcpCGWWMTHvs02Z88lxqlwvRz1joopn8u2mq_M0fIVJneY5n_tvnWZj2PmewN1CSORjBp3mY-sJEuABnh7Tx5kjAWdlFDAaVpXsB-bRBu_WOhjliCewGT6Sn7Q4BHGjrW9oSE2iCDg09bZ_TuQjXx0dXByfMF1pgmh68z7gqE0y5KU2IKVrCQkxixQ2K0gbeNOGspNSiMELFok5emdJRWYRxIbgm_yJegjG6OS5DkKFS9QxlmXCTRGikTkwqChoZSq5CGdaAD99xrj0Lue3pY17xJ1tccsIld7jkvAZbn9c8Dzg4_jx7bQhG7r_HXl4hUYPtIZzV4d9bW_m7tVWYjJwG2WmZNRjrd19xHSb0W7_V627AqLi93_A6SXungpE8Dw-sjJpWikuSzfSB5MXlzQfpvuyD |
| linkProvider | ProQuest |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1LT9wwEB5RqFQ48GiLWB7FB3pqrcZxEq8PCCEeArGseqASt9SxJxISy8Lu8vpT_EbG3oQAUrlx6C1SEifOfPOwJ_MNwEZmTJEqX90eJ8gTbSRvl7bgKtXCSV1QhBwk3VHdbvv0VP-egIe6Fsb_VlnbxGCoXd_6PfJf5EgyJYQSeuvyivuuUT67WrfQGMPiCO9vack23DzcJfl-j-P9vZOdA151FeBWZnLEhSkTTIUrXYQpenY-TKQRDlXps0yWJmW0tqpwykjVphDE2LgsIlkoYcmZShr3A0wltPDyenUc7TQkvyo0RIt0nHEKJGRVpFOV6qX-5yRa-kUhdypeOsImun2VkA1-bn_uf_tC8zBbRdRse6wCCzCBF59h5hnP4hfo7NLBTaA45-UAkY37Zg8ZReysd3aHjgfaDBywC9LCXp_gy6yPnH0DDXSsT4a1V1WsfoU_7zKdRZikh-MSsAyNaWeoy0S4JEanbeJSVZDdK4WJdNQCUcs0txXHun_T87xhh_Y4yAkHecBBLlrw4-meyzHDyJtXr9bCzytrM8wbybfgZw2f5vS_R1t-e7R1-HRwctzJO4fdoxWYjgN6_QbUKkyOBte4Bh_tzehsOPgW9IDB3_eG1SN6t0L3 |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Nb9QwEB2VFqFyoHxVXdqCD3ACq3GcxPGhQhXbFVVXqz2AVHEJjj2WKrHddncp8Nf4dYy9SQOV6K2H3iIlcWL7eWbsmXkD8Lowps5VyG5PM-SZNpKX3tZc5Vo4qWuykONMD9VoVJ6c6PEK_G5zYUJYZSsTo6B2UxvOyPdIkRRKCCX0nm_CIsb9wfvzCx4qSAVPa1tOYwmRY_z1g7Zv8_2jPs31mzQdHH768JE3FQa4lYVccGF8hrlw3iWYY2Dqw0wa4VD54HGy1EGjtVW1U0aqkswRY1NfJ7JWwpJildTuPVhTWVGGcLJx_qUj_FWxOFqi04KTUSGbhJ0mbS8PgUq0DUyiH1X8qxQ7S_eaczbqvMHGXR6tx_CosbTZwXJpPIEVPHsKD__iX3wGwz5dXEbqc-5niGxZT3vOyJJnk9Of6Hik08AZO6PVOZkSrJkNFnUorIGOTUngTppM1ufw-Va6swmr9HHcAlagMWWB2mfCZSk6bTOXq5rkoRcm0UkPRDu_lW2418Offqs61uiAiYowUUVMVKIHb6_eOV8yj9z49E4LhKqRQvOqQ0EP3rVQ6m7_v7UXN7f2Ch4Qmqrh0eh4G9bTCORwLrUDq4vZd9yF-_ZycTqfvYxLgsHX20bVH7VZTAc |
| 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=Derivative-free+methods+for+mixed-integer+nonsmooth+constrained+optimization&rft.jtitle=Computational+optimization+and+applications&rft.au=Giovannelli%2C+Tommaso&rft.au=Liuzzi%2C+Giampaolo&rft.au=Lucidi%2C+Stefano&rft.au=Rinaldi%2C+Francesco&rft.date=2022-06-01&rft.pub=Springer+Nature+B.V&rft.issn=0926-6003&rft.eissn=1573-2894&rft.volume=82&rft.issue=2&rft.spage=293&rft.epage=327&rft_id=info:doi/10.1007%2Fs10589-022-00363-1&rft.externalDBID=HAS_PDF_LINK |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0926-6003&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0926-6003&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0926-6003&client=summon |