Outer approximation algorithms for canonical DC problems
The paper discusses a general framework for outer approximation type algorithms for the canonical DC optimization problem. The algorithms rely on a polar reformulation of the problem and exploit an approximated oracle in order to check global optimality. Consequently, approximate optimality conditio...
Saved in:
| Published in: | Journal of global optimization Vol. 46; no. 2; pp. 163 - 189 |
|---|---|
| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Boston
Springer US
01.02.2010
Springer Nature B.V |
| Subjects: | |
| ISSN: | 0925-5001, 1573-2916 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | The paper discusses a general framework for outer approximation type algorithms for the canonical DC optimization problem. The algorithms rely on a polar reformulation of the problem and exploit an approximated oracle in order to check global optimality. Consequently, approximate optimality conditions are introduced and bounds on the quality of the approximate global optimal solution are obtained. A thorough analysis of properties which guarantee convergence is carried out; two families of conditions are introduced which lead to design six implementable algorithms, whose convergence can be proved within a unified framework. |
|---|---|
| AbstractList | The paper discusses a general framework for outer approximation type algorithms for the canonical DC optimization problem. The algorithms rely on a polar reformulation of the problem and exploit an approximated oracle in order to check global optimality. Consequently, approximate optimality conditions are introduced and bounds on the quality of the approximate global optimal solution are obtained. A thorough analysis of properties which guarantee convergence is carried out; two families of conditions are introduced which lead to design six implementable algorithms, whose convergence can be proved within a unified framework.[PUBLICATION ABSTRACT] The paper discusses a general framework for outer approximation type algorithms for the canonical DC optimization problem. The algorithms rely on a polar reformulation of the problem and exploit an approximated oracle in order to check global optimality. Consequently, approximate optimality conditions are introduced and bounds on the quality of the approximate global optimal solution are obtained. A thorough analysis of properties which guarantee convergence is carried out; two families of conditions are introduced which lead to design six implementable algorithms, whose convergence can be proved within a unified framework. |
| Author | Bigi, Giancarlo Zhang, Qinghua Frangioni, Antonio |
| Author_xml | – sequence: 1 givenname: Giancarlo surname: Bigi fullname: Bigi, Giancarlo email: giancarlo.bigi@di.unipi.it, bigig@di.unipi.it organization: Dipartimento di Informatica, Università di Pisa – sequence: 2 givenname: Antonio surname: Frangioni fullname: Frangioni, Antonio organization: Dipartimento di Informatica, Università di Pisa, Polo Universitario della Spezia – sequence: 3 givenname: Qinghua surname: Zhang fullname: Zhang, Qinghua organization: Dipartimento di Informatica, Università di Pisa |
| BookMark | eNp9kLFOwzAQhi1UJNrCA7BF7IazHSf2iAoUpEpdYLYcxy6p0rjYrgRvj0sYEBJMt3zf_Xf_DE0GP1iELglcE4D6JhIQUmAAiWVJOCYnaEp4zTCVpJqgKUjKMQcgZ2gW4xYyKDidIrE-JBsKvd8H_97tdOr8UOh-40OXXnexcD4URuewzui-uFsUmWt6u4vn6NTpPtqL7zlHLw_3z4tHvFovnxa3K2wYFwm3sq2NgJLaEqhrrCGtpnUFmjpnOXPM0la6homKO80Yo4baVlRtK1lVsqZhc3Q17s3Bbwcbk9r6QxhypCKyrDjUrMxQPUIm-BiDdcp06euXFHTXKwLq2JIaW1L5eXVsSZFskl_mPuQawse_Dh2dmNlhY8OPk_6UPgFNq3vf |
| CitedBy_id | crossref_primary_10_1007_s10288_010_0126_8 crossref_primary_10_1007_s10898_019_00833_7 crossref_primary_10_1007_s10957_012_0069_7 crossref_primary_10_1007_s10898_012_9908_1 |
| Cites_doi | 10.1080/02331938808843381 10.1016/0377-2217(90)90250-F 10.1109/TIP.2008.2003406 10.1007/BF01586935 10.1007/BF01097005 10.1023/A:1008260227877 10.1007/BF01580762 10.1007/BF01099647 10.1007/BF00120663 10.1007/BF00938217 10.1016/S0304-0208(08)72403-4 10.1016/0167-6377(95)00037-X 10.1023/A:1008331305949 10.1137/S105262349935178X 10.1007/BF02283685 10.1007/BF00122050 10.1023/A:1024700901538 10.1007/BF01098360 10.1016/S0167-6377(99)00074-7 10.1023/A:1008217604285 10.1007/BF00121302 10.1515/9781400873173 10.1007/978-1-4615-2025-2_4 10.1007/BFb0121159 10.1007/978-1-4757-2809-5 10.1007/978-3-662-02598-7 |
| ContentType | Journal Article |
| Copyright | Springer Science+Business Media, LLC. 2009 Springer Science+Business Media, LLC. 2010 |
| Copyright_xml | – notice: Springer Science+Business Media, LLC. 2009 – notice: Springer Science+Business Media, LLC. 2010 |
| 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/s10898-009-9415-1 |
| DatabaseName | CrossRef ProQuest Central (Corporate) Computer and Information Systems Abstracts ABI/INFORM Collection ABI/INFORM Global (PDF only) ProQuest Central (purchase pre-March 2016) ABI/INFORM Collection Science Database (Alumni Edition) Computing Database (Alumni Edition) ProQuest Pharma Collection Technology Research Database ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central (Alumni) (purchase pre-March 2016) ABI/INFORM Collection (Alumni) Research Library (Alumni) Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection ProQuest Central Essentials - QC ProQuest Central Business Premium Collection ProQuest Technology Collection ProQuest One ProQuest Central Korea 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 (New) ProQuest One Academic Middle East (New) ProQuest One Business 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 | 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 | 189 |
| ExternalDocumentID | 1935395811 10_1007_s10898_009_9415_1 |
| 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-c358t-d9d7c8042e402fbec1da2760a2ffe53f3e2d9fb3865fa3332c2ed86dd93643bb3 |
| IEDL.DBID | M2P |
| ISICitedReferencesCount | 5 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000273403000001&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 | Tue Nov 04 16:25:26 EST 2025 Tue Nov 18 22:01:13 EST 2025 Sat Nov 29 01:59:28 EST 2025 Fri Feb 21 02:42:32 EST 2025 |
| IsDoiOpenAccess | false |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 2 |
| Keywords | Polar set Cutting plane algorithms DC problems Approximate optimality conditions |
| Language | English |
| License | http://www.springer.com/tdm |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c358t-d9d7c8042e402fbec1da2760a2ffe53f3e2d9fb3865fa3332c2ed86dd93643bb3 |
| Notes | SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 |
| OpenAccessLink | http://link.springer.com/article/10.1007/s10898-009-9415-1 |
| PQID | 194650734 |
| PQPubID | 29930 |
| PageCount | 27 |
| ParticipantIDs | proquest_journals_194650734 crossref_citationtrail_10_1007_s10898_009_9415_1 crossref_primary_10_1007_s10898_009_9415_1 springer_journals_10_1007_s10898_009_9415_1 |
| PublicationCentury | 2000 |
| PublicationDate | 20100200 2010-2-00 20100201 |
| PublicationDateYYYYMMDD | 2010-02-01 |
| PublicationDate_xml | – month: 2 year: 2010 text: 20100200 |
| 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 | 2010 |
| Publisher | Springer US Springer Nature B.V |
| Publisher_xml | – name: Springer US – name: Springer Nature B.V |
| References | Fulop (CR7) 1990; 44 Ryoo, Sahinidis (CR15) 2003; 26 Androulakis, Maranas, Floudas (CR2) 1995; 7 Nghia, Hieu (CR11) 1986; 11 Horst, Pardalos (CR10) 1995 Tuy, Horst, Pardalos (CR29) 1995 Rockafellar (CR16) 1970 Thach (CR18) 1985; 10 CR35 Tuy (CR26) 1991; 1 Tuy, Horst (CR24) 1988; 41 Strekalovsky, Tsevendorj (CR17) 1998; 13 Pintér (CR13) 2006 Chapelle, Sindhwani, Keerthi (CR6) 2008; 9 Tuy (CR27) 1992; 2 Tuy (CR23) 1987; 52 Tuy, Tam (CR33) 1995; 20 Tuy (CR25) 1991; 51 Tuy (CR30) 1998 Grippo, Sciandrone (CR8) 2000; 26 Horst, Tuy (CR9) 1990 Tuy (CR28) 1995; 18 Ben Saad, Floudas, Pardalos (CR3) 1992 Ben Saad, Jacobsen (CR4) 1990; 25 Thoai (CR19) 1988; 19 Tuy, Al-Khayyal (CR31) 1992; 2 Ben Saad, Jacobsen (CR5) 1994; 5 Tuy, Hiriart- Urruty (CR22) 1986 Tuy (CR21) 1987; 30 Pham, El Bernoussi (CR12) 1989; 87 Tuy, Migdalas, Varbrand (CR32) 1994; 4 Rikun (CR14) 1997; 10 Tuan (CR20) 2000; 16 Wen, Ng, Huang (CR34) 2008; 17 Al-Khayyal, Sherali (CR1) 2000; 10 H. Tuy (9415_CR23) 1987; 52 S. Ben Saad (9415_CR3) 1992 P.T. Thach (9415_CR18) 1985; 10 9415_CR35 S. Ben Saad (9415_CR5) 1994; 5 A.D. Rikun (9415_CR14) 1997; 10 H. Tuy (9415_CR30) 1998 L. Grippo (9415_CR8) 2000; 26 H. Tuy (9415_CR25) 1991; 51 H.D. Tuan (9415_CR20) 2000; 16 H. Tuy (9415_CR24) 1988; 41 R.T. Rockafellar (9415_CR16) 1970 (9415_CR13) 2006 Y.-W. Wen (9415_CR34) 2008; 17 H. Tuy (9415_CR32) 1994; 4 J. Fulop (9415_CR7) 1990; 44 (9415_CR10) 1995 S. Ben Saad (9415_CR4) 1990; 25 H. Tuy (9415_CR31) 1992; 2 D.T. Pham (9415_CR12) 1989; 87 H. Tuy (9415_CR29) 1995 I. Androulakis (9415_CR2) 1995; 7 M.D. Nghia (9415_CR11) 1986; 11 H. Tuy (9415_CR28) 1995; 18 F. Al-Khayyal (9415_CR1) 2000; 10 H. Ryoo (9415_CR15) 2003; 26 H. Tuy (9415_CR22) 1986 A.S. Strekalovsky (9415_CR17) 1998; 13 H. Tuy (9415_CR33) 1995; 20 N.V. Thoai (9415_CR19) 1988; 19 H. Tuy (9415_CR21) 1987; 30 O. Chapelle (9415_CR6) 2008; 9 H. Tuy (9415_CR26) 1991; 1 H. Tuy (9415_CR27) 1992; 2 R. Horst (9415_CR9) 1990 |
| References_xml | – volume: 19 start-page: 665 year: 1988 end-page: 674 ident: CR19 article-title: A modified version of Tuy’s method for solving DC programming problems publication-title: Optimization doi: 10.1080/02331938808843381 – volume: 44 start-page: 395 year: 1990 end-page: 409 ident: CR7 article-title: A finite cutting plane method for solving linear programs with an additional reverse constraint publication-title: European J. Oper. Res. doi: 10.1016/0377-2217(90)90250-F – start-page: 152 year: 1992 end-page: 164 ident: CR3 article-title: A new cutting plane algorithm for a class of reverse convex 0–1 integer programs publication-title: Recent advances in global optimization – volume: 17 start-page: 2081 year: 2008 end-page: 2088 ident: CR34 article-title: Efficient total variation minimization methods for color image restoration publication-title: IEEE Trans. Image Process. doi: 10.1109/TIP.2008.2003406 – volume: 51 start-page: 229 year: 1991 end-page: 245 ident: CR25 article-title: Normal conical algorithm for concave minimization over polytopes publication-title: Math. Program. doi: 10.1007/BF01586935 – volume: 11 start-page: 241 year: 1986 end-page: 252 ident: CR11 article-title: A method for solving reverse convex programming problems publication-title: Acta Math. Vietnam. – volume: 5 start-page: 95 year: 1994 end-page: 96 ident: CR5 article-title: Comments on a reverse convex programming algorithm publication-title: J. Global Optim. doi: 10.1007/BF01097005 – volume: 10 start-page: 35 year: 1985 end-page: 57 ident: CR18 article-title: Convex programs with several additional reverse convex constraints publication-title: Acta Math. Vietnam. – volume: 13 start-page: 61 year: 1998 end-page: 74 ident: CR17 article-title: Testing the -strategy for a reverse convex problem publication-title: J. Global Optim. doi: 10.1023/A:1008260227877 – volume: 87 start-page: 97 year: 1989 end-page: 132 ident: CR12 article-title: Numerical methods for solving a class of global nonconvex optimization problems publication-title: Int. Ser. Numer. Math. – volume: 41 start-page: 161 year: 1988 end-page: 183 ident: CR24 article-title: Convergence and restart in branch-and-bound algorithms for global optimization. Application to concave minimization and DC optimization problems publication-title: Math. Program. doi: 10.1007/BF01580762 – volume: 7 start-page: 337 year: 1995 end-page: 363 ident: CR2 article-title: –BB: a global optimization method for general constrained nonconvex problems publication-title: J. Global Optim. doi: 10.1007/BF01099647 – volume: 1 start-page: 23 year: 1991 end-page: 36 ident: CR26 article-title: Effect of the subdivision strategy on convergence and efficiency of some global optimization algorithms publication-title: J. Global Optim. doi: 10.1007/BF00120663 – volume: 52 start-page: 463 year: 1987 end-page: 486 ident: CR23 article-title: Convex programs with an additional reverse convex constraint publication-title: J. Optim. Theory Appl. doi: 10.1007/BF00938217 – volume: 20 start-page: 99 year: 1995 end-page: 114 ident: CR33 article-title: Polyhedral annexation vs outer approximation for the decomposition of monotonic quasiconcave minimization problems publication-title: Acta Math. Vietnam. – ident: CR35 – year: 1998 ident: CR30 publication-title: Convex analysis and global optimization – year: 1995 ident: CR10 publication-title: Handbook of global optimization – year: 2006 ident: CR13 publication-title: Global optimization: scientific and engineering case studies – start-page: 273 year: 1986 end-page: 303 ident: CR22 article-title: A general deterministic approach to global optimization via DC programming publication-title: FERMAT Days 85: mathematics for optimization doi: 10.1016/S0304-0208(08)72403-4 – volume: 18 start-page: 99 year: 1995 end-page: 106 ident: CR28 article-title: Canonical DC programming problem: outer approximation methods revisited publication-title: Oper. Res. Lett. doi: 10.1016/0167-6377(95)00037-X – volume: 30 start-page: 150 year: 1987 end-page: 182 ident: CR21 article-title: Global minimization of a difference of two convex functions publication-title: Math. Program. Stud. – volume: 16 start-page: 295 year: 2000 end-page: 297 ident: CR20 article-title: Remarks on an algorithm for reverse convex programs publication-title: J. Global Optim. doi: 10.1023/A:1008331305949 – volume: 10 start-page: 1049 year: 2000 end-page: 1057 ident: CR1 article-title: On finitely terminating branch-and-bound algorithms for some global optimization problems publication-title: SIAM J. Optim. doi: 10.1137/S105262349935178X – volume: 25 start-page: 19 year: 1990 end-page: 42 ident: CR4 article-title: A level set algorithm for a class of reverse convex programs publication-title: Ann. Oper. Res. doi: 10.1007/BF02283685 – volume: 2 start-page: 133 year: 1992 end-page: 144 ident: CR27 article-title: On nonconvex optimization problems with separated nonconvex variables publication-title: J. Global Optim. doi: 10.1007/BF00122050 – volume: 26 start-page: 387 year: 2003 end-page: 418 ident: CR15 article-title: Global optimization of multiplicative programs publication-title: J. Global Optim. doi: 10.1023/A:1024700901538 – year: 1970 ident: CR16 publication-title: Convex analysis – volume: 4 start-page: 243 year: 1994 end-page: 263 ident: CR32 article-title: A quasiconcave minimization method for solving linear two-level programs publication-title: J. Global Optim. doi: 10.1007/BF01098360 – volume: 26 start-page: 127 year: 2000 end-page: 136 ident: CR8 article-title: On the convergence of the block nonlinear Gauss–Seidel method under convex constraints publication-title: Oper. Res. Lett. doi: 10.1016/S0167-6377(99)00074-7 – volume: 9 start-page: 203 year: 2008 end-page: 233 ident: CR6 article-title: Optimization techniques for semi-supervised support vector machines publication-title: J. Mach. Learn. Res. – volume: 10 start-page: 425 year: 1997 end-page: 437 ident: CR14 article-title: A convex envelope formula for multilinear functions publication-title: J. Global Optim. doi: 10.1023/A:1008217604285 – start-page: 149 year: 1995 end-page: 216 ident: CR29 article-title: DC optimization: theory, methods and algorithms publication-title: Handbook of global optimization – volume: 2 start-page: 61 year: 1992 end-page: 71 ident: CR31 article-title: Global optimization of a nonconvex single facility location problem by sequential unconstrained convex minimization publication-title: J. Global Optim. doi: 10.1007/BF00121302 – year: 1990 ident: CR9 publication-title: Global optimization – volume: 41 start-page: 161 year: 1988 ident: 9415_CR24 publication-title: Math. Program. doi: 10.1007/BF01580762 – volume: 5 start-page: 95 year: 1994 ident: 9415_CR5 publication-title: J. Global Optim. doi: 10.1007/BF01097005 – volume-title: Convex analysis year: 1970 ident: 9415_CR16 doi: 10.1515/9781400873173 – start-page: 152 volume-title: Recent advances in global optimization year: 1992 ident: 9415_CR3 – volume-title: Global optimization: scientific and engineering case studies year: 2006 ident: 9415_CR13 – volume: 10 start-page: 35 year: 1985 ident: 9415_CR18 publication-title: Acta Math. Vietnam. – start-page: 149 volume-title: Handbook of global optimization year: 1995 ident: 9415_CR29 doi: 10.1007/978-1-4615-2025-2_4 – volume: 2 start-page: 61 year: 1992 ident: 9415_CR31 publication-title: J. Global Optim. doi: 10.1007/BF00121302 – volume: 19 start-page: 665 year: 1988 ident: 9415_CR19 publication-title: Optimization doi: 10.1080/02331938808843381 – volume: 87 start-page: 97 year: 1989 ident: 9415_CR12 publication-title: Int. Ser. Numer. Math. – start-page: 273 volume-title: FERMAT Days 85: mathematics for optimization year: 1986 ident: 9415_CR22 doi: 10.1016/S0304-0208(08)72403-4 – volume: 17 start-page: 2081 year: 2008 ident: 9415_CR34 publication-title: IEEE Trans. Image Process. doi: 10.1109/TIP.2008.2003406 – volume: 52 start-page: 463 year: 1987 ident: 9415_CR23 publication-title: J. Optim. Theory Appl. doi: 10.1007/BF00938217 – volume: 26 start-page: 127 year: 2000 ident: 9415_CR8 publication-title: Oper. Res. Lett. doi: 10.1016/S0167-6377(99)00074-7 – volume: 30 start-page: 150 year: 1987 ident: 9415_CR21 publication-title: Math. Program. Stud. doi: 10.1007/BFb0121159 – volume-title: Handbook of global optimization year: 1995 ident: 9415_CR10 – volume: 10 start-page: 425 year: 1997 ident: 9415_CR14 publication-title: J. Global Optim. doi: 10.1023/A:1008217604285 – volume: 4 start-page: 243 year: 1994 ident: 9415_CR32 publication-title: J. Global Optim. doi: 10.1007/BF01098360 – volume: 10 start-page: 1049 year: 2000 ident: 9415_CR1 publication-title: SIAM J. Optim. doi: 10.1137/S105262349935178X – volume: 25 start-page: 19 year: 1990 ident: 9415_CR4 publication-title: Ann. Oper. Res. doi: 10.1007/BF02283685 – volume: 1 start-page: 23 year: 1991 ident: 9415_CR26 publication-title: J. Global Optim. doi: 10.1007/BF00120663 – volume: 11 start-page: 241 year: 1986 ident: 9415_CR11 publication-title: Acta Math. Vietnam. – volume: 51 start-page: 229 year: 1991 ident: 9415_CR25 publication-title: Math. Program. doi: 10.1007/BF01586935 – volume: 9 start-page: 203 year: 2008 ident: 9415_CR6 publication-title: J. Mach. Learn. Res. – volume: 2 start-page: 133 year: 1992 ident: 9415_CR27 publication-title: J. Global Optim. doi: 10.1007/BF00122050 – ident: 9415_CR35 – volume: 26 start-page: 387 year: 2003 ident: 9415_CR15 publication-title: J. Global Optim. doi: 10.1023/A:1024700901538 – volume-title: Convex analysis and global optimization year: 1998 ident: 9415_CR30 doi: 10.1007/978-1-4757-2809-5 – volume: 44 start-page: 395 year: 1990 ident: 9415_CR7 publication-title: European J. Oper. Res. doi: 10.1016/0377-2217(90)90250-F – volume-title: Global optimization year: 1990 ident: 9415_CR9 doi: 10.1007/978-3-662-02598-7 – volume: 7 start-page: 337 year: 1995 ident: 9415_CR2 publication-title: J. Global Optim. doi: 10.1007/BF01099647 – volume: 13 start-page: 61 year: 1998 ident: 9415_CR17 publication-title: J. Global Optim. doi: 10.1023/A:1008260227877 – volume: 20 start-page: 99 year: 1995 ident: 9415_CR33 publication-title: Acta Math. Vietnam. – volume: 16 start-page: 295 year: 2000 ident: 9415_CR20 publication-title: J. Global Optim. doi: 10.1023/A:1008331305949 – volume: 18 start-page: 99 year: 1995 ident: 9415_CR28 publication-title: Oper. Res. Lett. doi: 10.1016/0167-6377(95)00037-X |
| SSID | ssj0009852 |
| Score | 1.9051374 |
| Snippet | The paper discusses a general framework for outer approximation type algorithms for the canonical DC optimization problem. The algorithms rely on a polar... |
| SourceID | proquest crossref springer |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 163 |
| SubjectTerms | Algorithms Approximation Computer Science Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Real Functions Studies |
| SummonAdditionalLinks | – databaseName: Springer Online Journals dbid: RSV link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LT8MwDLbQ4AAHxgaIMUA5cOChSF3TrskRDSYuDMRLu1VNk8CkwdA6ED8fp023gQAJjlUTt7Lj2Fbi7wPYt7xGCU84VUIqGshAU-mFkgqD0RYrEosvkpNNRL0e7_fFlevjzsrb7uWRZL5TzzW7cdsO5gkqMOpQLHkWMdpxy9dwfXM_Q9rlOc2OJ_yQhrgJl0eZ34n4HIxmGeaXQ9E81nSr__rLNVh1qSU5KdZCDRb0cx2qJW0DcV5ch5U5DEJ8upgCt2Z1qLlRGTlwgNSH68AvcwE5_Pj7oOh1JMnwYTQeTB6fMoJ5L0ELjfIWS3LaIY6lJtuAu-7ZbeecOsYFmrKQT9BgKko5-rHGstKgeVsq8SO0pm-MDplh2lfCSMsTahLGmJ_6WvG2UoJhZiMl24QKfk1vAWEoUXtBIDF7DxIphWGpURELWyxN2lI1wCtVH6cOjtyyYgzjGZCyVWWMqoytKuNWA46mU14KLI7fBjdLe8bOLbO4JQLMSCMWNOC4NN_c259kbf9pdBOWiysG9s7LDlQm41e9C0vp22SQjffyxfoB1yDiXw priority: 102 providerName: Springer Nature |
| Title | Outer approximation algorithms for canonical DC problems |
| URI | https://link.springer.com/article/10.1007/s10898-009-9415-1 https://www.proquest.com/docview/194650734 |
| Volume | 46 |
| WOSCitedRecordID | wos000273403000001&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 (ProQuest) 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: Springer Online Journals 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/eLvHCXMwpV1LT4QwEJ7o6kEPvo3rKz148JFGoCDtyeiqMTGuxLdeCKWtmvhYZTX-fKdQXDXRi5dJCNASPtqZ0pnvA1iyukYZzzhVQioaylBT6UWSCoPeFlckll-kFJuI221-eSkSl5tTuLTKek4sJ2r1lNt_5Ou42MZgImbhZueZWtEou7nqFDT6YQADG99mdB0GSY9zl5eCO54IIhrhdFxvalaVc9zWlnmCCnRh1P_ulnqx5o_t0dLr7I3-83nHYMSFm2Sr-j7GoU8_TsDwFxLCCRh3w7sgy46DemUS-JGVeiAl4_j7XVXeSLL7G-yie_tQEAx1CYLyVFZVkp0WccI0xRSc7e2etvapE1mgOYt4FzFScc5x6GpcSRpE1FdZECOAgTE6YobpQAkjrTSoyRhjQR5oxTeUEgyDGSnZNDSwNz0DhGGL2gtDiQF7mEkpDMuNilnkszzbkKoJXv2O09wxkFshjPu0x51sYUkRltTCkvpNWP28pVPRb_x18VwNRepGYpF-4tCEtRrLL2d_a2v2z7bmYKjKIrBpLfPQ6L686gUYzN-6d8XLIvTHF1eLMLC9206O8eggpmgPvZa1wVFpE2vjE7RJdI32-OT8AyuQ6bE |
| linkProvider | ProQuest |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3JTsMwEB2xScCBHVFWH0BikUVqJ8Q-IIQoVSugcACJW4hjG5DYU7aP4h8ZZ6GABDcOnJM4cfwySzzzHsCi0zWKRSyolkpTX_mGKi9QVFr0tpiROH6RTGwibLXE6ak86oK3shfGlVWWNjEz1Po2cf_I1zHZxmAi5P7W3T11olFuc7VU0MhRsWdenzFjSzebNVzeJcbqu8c7DVqICtCEB6KNz6TDRCBUDWZOFmdQ1TEL8YGZtSbglhumpVVOCtPGnHOWMKPFhtaSo_NWiuO43dDrO2IxVynIjjocvyIT-PEkC2iA5r_cRM079YTrZfMklegyafWrG-zEtt-2YzMvVx_-Z-9nBIaKcJps5_gfhS5zMwaDn0gWx2C0MF8pWS44tlfGQRw6KQuSMaq_XObtmyS-OscptS-uU4KhPEHQ3WZdo6S2QwrhnXQCTv5kPpPQg3czU0A4jmg831eYkPixUtLyxOqQB1WexBtKV8Ar1zRKCoZ1J_RxFXW4oR0MIoRB5GAQVSuw-nHJXU4v8tvJM-XSR4WlSaOPda_AWomdT0d_Gmv617EWoL9xfLAf7TdbezMwkFdMuBKeWehpPzyaOehLntqX6cN89gUQOPtrSL0DqXlASg |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3JTsMwEB2xCcGBHVFWH0BikdU0Toh9QAhRKhCo9AAS4hLi2AYk9oTt0_g7xllaQIJbD5yTTOz4eZZ4Zh7AsuU1injEqRJSUU96mkrHl1QYtLYYkdj-IhnZRNBs8rMz0eqBj7IWxqZVljoxU9TqPrb_yKsYbKMzETCvaoqsiFa9sf3wSC2BlD1oLdk0coQc6vdXjN6SrYM6LvWK6zb2Tnb3aUEwQGPm8xTHp4KYI2w1RlEGZ1NTkRvg4F1jtM8M064SRlpaTBMxxtzY1YpvKiUYGnIpGcrthf4AQ0ybTdjyzzv9fnlG9uMI16c-moLyQDWv2uO2rs0RVKD5pLXvJrHj5_44ms0sXmP0H3-rMRgp3Gyyk--LcejRdxMw_KX54gSMF2otIatF7-21SeDHluKCZJ3W367zsk4S3VzilNKr24Sgi08QjPdZNSmp75KCkCeZgtOuzGca-vBtegYIQ4na8TyJgYoXSSkMi40KmF9jcbQpVQWccn3DuOi8bglAbsJOz2gLiRAhEVpIhLUKrLcfecjbjvx181wJg7DQQEnYxkAFNkocfbn6m6zZP2UtwSAiKTw6aB7OwVCeSGEze-ahL3161gswEL-k18nTYrYZCFx0G1GfYV9JNg |
| 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=Outer+approximation+algorithms+for+canonical+DC+problems&rft.jtitle=Journal+of+global+optimization&rft.au=Bigi%2C+Giancarlo&rft.au=Frangioni%2C+Antonio&rft.au=Zhang%2C+Qinghua&rft.date=2010-02-01&rft.pub=Springer+Nature+B.V&rft.issn=0925-5001&rft.eissn=1573-2916&rft.volume=46&rft.issue=2&rft.spage=163&rft_id=info:doi/10.1007%2Fs10898-009-9415-1&rft.externalDBID=HAS_PDF_LINK&rft.externalDocID=1935395811 |
| 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 |