An approximation method for the optimization of continuous functions of n variables by densifying their domains
Most of the known optimization methods for a given continuous function f defined on a compact set H = i=1,..,n[ai,bi] require strong conditions on f. In the early 1980s, Cherruault proposed a method, called ALIENOR which was able to reduce the multidimensional optimization problem to another one-dim...
Saved in:
| Published in | Kybernetes Vol. 28; no. 2; pp. 164 - 180 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
London
MCB UP Ltd
01.03.1999
Emerald Group Publishing Limited |
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | Most of the known optimization methods for a given continuous function f defined on a compact set H = i=1,..,n[ai,bi] require strong conditions on f. In the early 1980s, Cherruault proposed a method, called ALIENOR which was able to reduce the multidimensional optimization problem to another one-dimensional optimization: the optimization of the restriction fh* of f to some adequate -dense curve h into the domain H. The characterization, the generation of such curves as well as the theoretic calculation times associated with them, have been studied previously by the authors. Their consequences and the general problem concerning the error in the approximation to global minimum of f and the minimization of the error itself, that such reduction produces, will be the subject of this paper. |
|---|---|
| AbstractList | The reduction of a multidimensional problem to a one-dimensional one, depending on the specific context where it is used, can be found in a very large class of mathematical situations. This is focused on a middle level between two old problems, namely, the space-filling curves such as the Peano, Hilbert, Sierpinski curves and so on, and the problem consisting of the representation of a continuous function defined on an n-dimensional cube. Most of the known optimization methods for a given continuous function f defined on a compact set H i1,..,nai,bi require strong conditions on f. In the early 1980s, Cherruault proposed a method, called ALIENOR which was able to reduce the multidimensional optimization problem to another onedimensional optimization the optimization of the restriction fh of f to some adequate dense curve h into the domain H. The characterization, the generation of such curves as well as the theoretic calculation times associated with them, have been studied previously by the authors. Their consequences and the general problem concerning the error in the approximation to global minimum of f and the minimization of the error itself, that such reduction produces, will be the subject of this paper. Most of the known optimization methods for a given continuous function f defined on a compact set H = i=1,..,n[ai,bi] require strong conditions on f. In the early 1980s, Cherruault proposed a method, called ALIENOR which was able to reduce the multidimensional optimization problem to another one-dimensional optimization: the optimization of the restriction fh* of f to some adequate -dense curve h into the domain H. The characterization, the generation of such curves as well as the theoretic calculation times associated with them, have been studied previously by the authors. Their consequences and the general problem concerning the error in the approximation to global minimum of f and the minimization of the error itself, that such reduction produces, will be the subject of this paper. |
| Author | Cherruault, Yves Mora, Gaspar |
| Author_xml | – sequence: 1 givenname: Gaspar surname: Mora fullname: Mora, Gaspar organization: Department of Mathematical Analysis and Applied Mathematics, Faculty of Sciences, University of Alicante, Spain, and – sequence: 2 givenname: Yves surname: Cherruault fullname: Cherruault, Yves organization: Université Pierre et Marie Curie - Paris VI, Paris, France |
| BookMark | eNp9kctu1TAQQC3UStwWPoCdxYYNAb9iO8uqFC6iEosWgdhYvo5NXRI72A7q5etxCOqiha5GmjlnNI8jcBBisAA8w-gVxki-RpRL1pGuw4i0UnTyEdhg0cpGSEkPwGapNxX48hgc5XyNECacoA2IJwHqaUrxxo-6-BjgaMtV7KGLCZYrC-NU_Oh_rbXooImh-DDHOUM3B7Ok85IP8KdOXu8Gm-FuD3sbsnd7H74tXXyCfRy1D_kJOHR6yPbp33gMPr09uzzdNucf370_PTlvDMOyNNI6bARHru0NN0Swtq5hebure2jmONe9lMT2fGcFkhQLy6nuGO5ptSQ29Bi8WPvW1X7MNhc1-mzsMOhg6-xKMEop56yt5PM75HWcU6jDKYJpvWfHRIXECpkUc07WKePLn5uUpP2gMFLLG9S9N1QT3zGnVE-d9g86zer4XOzNraDTd8UFFa1in4n6-oZst_gDVheVf7nydrRJD_2tca-1mnpXcfRv_P8T_QaOnLc3 |
| CODEN | KBNTA3 |
| CitedBy_id | crossref_primary_10_1016_S0898_1221_00_00085_7 crossref_primary_10_1108_03684920210419010 crossref_primary_10_1108_03684920310493369 crossref_primary_10_1007_s00009_017_0845_6 crossref_primary_10_1108_03684920010312803 crossref_primary_10_1108_03684920010333170 crossref_primary_10_1007_s00009_020_01585_5 crossref_primary_10_1108_03684920510605803 crossref_primary_10_1007_s13398_011_0005_y crossref_primary_10_1108_03684920710741260 crossref_primary_10_1142_S0218348X17500396 |
| Cites_doi | 10.1108/eb005845 10.1016/0895-7177(93)90003-H 10.1108/03684929810240347 10.1126/science.276.5315.1094 10.1090/trans2/028/04 10.1016/S0898-1221(97)00067-9 |
| ContentType | Journal Article |
| Copyright | MCB UP Limited Copyright MCB UP Limited (MCB) 1999 |
| Copyright_xml | – notice: MCB UP Limited – notice: Copyright MCB UP Limited (MCB) 1999 |
| DBID | BSCLL AAYXX CITATION 7SC 7SP 7TB 7XB 8AO 8FD 8FE 8FG AFKRA ARAPS AZQEC BENPR BGLVJ CCPQU DWQXO FR3 GNUQQ GUQSH HCIFZ JQ2 K7- L7M L~C L~D M0N M2O MBDVC P5Z P62 PHGZM PHGZT PKEHL PQEST PQGLB PQQKQ PQUKI PRINS Q9U |
| DOI | 10.1108/03684929910258798 |
| DatabaseName | Istex CrossRef Computer and Information Systems Abstracts Electronics & Communications Abstracts Mechanical & Transportation Engineering Abstracts ProQuest Central (purchase pre-March 2016) ProQuest Pharma Collection Technology Research Database ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central UK/Ireland Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Central Technology Collection (via ProQuest SciTech Premium Collection) ProQuest One Community College ProQuest Central Korea Engineering Research Database ProQuest Central Student ProQuest Research Library SciTech Premium Collection (via ProQuest) ProQuest Computer Science Collection Computer Science Database Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional Computing Database Research Library 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 Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic ProQuest One Academic UKI Edition ProQuest Central China ProQuest Central Basic |
| DatabaseTitle | CrossRef Research Library Prep Computer Science Database ProQuest Central Student Technology Collection Technology Research Database Computer and Information Systems Abstracts – Academic ProQuest One Academic Middle East (New) Mechanical & Transportation Engineering Abstracts ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection Computer and Information Systems Abstracts SciTech Premium Collection ProQuest One Community College ProQuest Pharma Collection ProQuest Central China ProQuest Central ProQuest One Applied & Life Sciences ProQuest Central Korea ProQuest Research Library ProQuest Central (New) Advanced Technologies Database with Aerospace Advanced Technologies & Aerospace Collection ProQuest Computing ProQuest Central Basic ProQuest One Academic Eastern Edition Electronics & Communications Abstracts ProQuest Technology Collection ProQuest SciTech Collection Computer and Information Systems Abstracts Professional Advanced Technologies & Aerospace Database ProQuest One Academic UKI Edition Engineering Research Database ProQuest One Academic ProQuest One Academic (New) |
| DatabaseTitleList | Technology Research Database Research Library Prep |
| Database_xml | – sequence: 1 dbid: 8FG name: ProQuest Technology Collection url: https://search.proquest.com/technologycollection1 sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Sciences (General) |
| EISSN | 1758-7883 |
| EndPage | 180 |
| ExternalDocumentID | 86063508 10_1108_03684929910258798 ark_67375_4W2_ZD2HH1K1_S 10.1108/03684929910258798 |
| Genre | Feature |
| GroupedDBID | 0R 1WG 29L 3FY 3V. 4.4 490 5GY 5VS 70U 8AO 8FE 8FG 8FW 8R4 8R5 9E0 AADTA AADXL AAGBP AAMCF AAPBV AATHL AAUDR ABIJV ABPTK ABSDC ACGFS ACIWK ACMTK ADOMW AEBZA AEDOK AENEX AEUCW AFKRA AFYHH AJEBP ALMA_UNASSIGNED_HOLDINGS ARAPS ASMFL ASPBG ATGMP AUCOK AVELQ AVWKF AZFZN AZQEC BENPR BFQZO BGLVJ BPHCQ BPQFQ BTXLY BUONS CAG COF CS3 DWQXO EBS ECCUG EJD FNNZZ GEI GEL GMN GNUQQ GQ. GUQSH H13 HCIFZ HZ IJT IPNFZ J1Y JI- JL0 K6V K7- M0N M2O M42 O9- P62 PADUT PQEST PQQKQ PQUKI PRG PRINS PROAC Q2X Q3A RIG ROL TDQ TEM TGG TMD TMF V1G Z11 Z12 .DC AAPSD ABEAN ABKQV ACZLT AEMMR AFNZV AODMV BSCLL HZ~ SBBZN SDURG AABYC AAPXH AAYXX ABJNI ABKIT ABXQL ABYQI ACZUD ADFIF ADIOT ADQUB ADYJY AEACZ AFNTC AFQLH AFVFF AFZLO AGQPQ AGUEF AHMHQ AJNYF AJZCB AKXVL ALJBP AMLIN ASJQZ CCPQU CITATION KBGRL PHGZM PHGZT PQGLB UGKUH 7SC 7SP 7TB 7XB 8FD FR3 JQ2 L7M L~C L~D MBDVC PKEHL Q9U |
| ID | FETCH-LOGICAL-c418t-8ef1c760f5dc6c2745883e65b036a4f66ad882ed6be708317e63a941d3c7681c3 |
| IEDL.DBID | BENPR |
| ISSN | 0368-492X |
| IngestDate | Fri Jul 11 06:38:41 EDT 2025 Fri Aug 22 07:41:01 EDT 2025 Thu Jul 31 00:10:56 EDT 2025 Thu Apr 24 23:10:06 EDT 2025 Wed Oct 30 09:16:00 EDT 2024 Wed Jul 31 14:17:22 EDT 2019 Tue Nov 23 15:45:40 EST 2021 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 2 |
| Keywords | Biocybernetics Global optimization Transformation Dense curve |
| Language | English |
| License | http://www.emeraldinsight.com/page/tdm |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c418t-8ef1c760f5dc6c2745883e65b036a4f66ad882ed6be708317e63a941d3c7681c3 |
| Notes | original-pdf:0670280202.pdf istex:C2C633587F575DE4B925AD4338FC2AC03FDF6C9B ark:/67375/4W2-ZD2HH1K1-S filenameID:0670280202 href:03684929910258798.pdf SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23 |
| PQID | 213910947 |
| PQPubID | 37993 |
| PageCount | 17 |
| ParticipantIDs | proquest_miscellaneous_743336645 crossref_citationtrail_10_1108_03684929910258798 istex_primary_ark_67375_4W2_ZD2HH1K1_S crossref_primary_10_1108_03684929910258798 proquest_journals_213910947 emerald_primary_10_1108_03684929910258798 |
| PublicationCentury | 1900 |
| PublicationDate | 1999-03-01 |
| PublicationDateYYYYMMDD | 1999-03-01 |
| PublicationDate_xml | – month: 03 year: 1999 text: 1999-03-01 day: 01 |
| PublicationDecade | 1990 |
| PublicationPlace | London |
| PublicationPlace_xml | – name: London |
| PublicationTitle | Kybernetes |
| PublicationYear | 1999 |
| Publisher | MCB UP Ltd Emerald Group Publishing Limited |
| Publisher_xml | – name: MCB UP Ltd – name: Emerald Group Publishing Limited |
| References | b2 b6 b14 b13 b16 b9 b1 |
| References_xml | – ident: b16 – ident: b6 doi: 10.1108/eb005845 – ident: b1 doi: 10.1016/0895-7177(93)90003-H – ident: b14 doi: 10.1108/03684929810240347 – ident: b2 doi: 10.1126/science.276.5315.1094 – ident: b9 doi: 10.1090/trans2/028/04 – ident: b13 doi: 10.1016/S0898-1221(97)00067-9 |
| SSID | ssj0012620 |
| Score | 1.5573926 |
| Snippet | Most of the known optimization methods for a given continuous function f defined on a compact set H = i=1,..,n[ai,bi] require strong conditions on f. In the... Most of the known optimization methods for a given continuous function f defined on a compact set H i1,..,nai,bi require strong conditions on f. In the early... The reduction of a multidimensional problem to a one-dimensional one, depending on the specific context where it is used, can be found in a very large class of... |
| SourceID | proquest crossref istex emerald |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 164 |
| SubjectTerms | Biocybernetics Cybernetics Dense curve Global optimization Mathematical models Methods Transformation |
| Title | An approximation method for the optimization of continuous functions of n variables by densifying their domains |
| URI | https://www.emerald.com/insight/content/doi/10.1108/03684929910258798/full/html https://api.istex.fr/ark:/67375/4W2-ZD2HH1K1-S/fulltext.pdf https://www.proquest.com/docview/213910947 https://www.proquest.com/docview/743336645 |
| Volume | 28 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV3db9MwED-x9oUXxAaIMJj8MBBDimgcx3ae0BgrFYgJARMVL1YSO1IFS8rSovHfc-e4QdukvjpnP_jO95H7-AEcFmglC5VPYo7qLxYZr-NS8TIuRVZyDN5qW1Fz8qczOTsXH-bZPNTmdKGscqMTvaK2bUX_yF9zdFUSjEXUm-XvmECjKLkaEDR2YIwaWOsRjN-enn3-MqQRaNp6n6zUscj5PKQ1PfQNruESukdo9bXK9TXD9L87d0y3fXVLU3vzM70P94LfyI57Ru_CHdfswW54mR17GcZHHz2A9rhhflL41aJvS2Q9SjRD95Shu8da1BIXof2StTWjavVFs27XHSMr5wWR1hv2BwNpaq3qWPmXWSp1911RzGcXmG0vikXTPYTz6em3k1kcYBXiSiR6FWtXJ5WSkzqzlawwKs20Tp3MSrySQtRSFhbdbmdl6RThkCkn0yIXiU1xl06q9BGMmrZxj4FpafNaEXSH04JbqblVNXXbukrmaH0jmGzu1FRh5jhBX_wyPvYgAMybbIjg1bBl2Q_c2Eb8PDBqoL1FY5a2juDoJt2WM194lg-UxeVPqn5TmRHfufnxjs9mycfEfI1gfyMTJjz8zgxiGgEbvuKLpTRM0ThkpUGfLU2lFNmTrQfsw91-RATVuz2F0epy7Z6hA7QqD2BHT98fBGH_B904_yw |
| linkProvider | ProQuest |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lb9QwEB6V9gAXRHmIUB4-UESRIjaO4zgHhCrKkrJtL7RixcVNYkdaQZOl2YX2R_EfmXEeiFbaW6_eiQ-Zycw3O48P4GWGUTKLk5HP0f35IuKln8c893MR5RyTt9IUNJx8eCTTE_F5Gk3X4E8_C0Ntlb1PdI7a1AX9R_6WI1QJMBeJ389_-kQaRcXVnkGjtYqJvfyNGVvzbn8P1bvN-fjj8YfU70gF_EIEauErWwZFLEdlZApZYE4WKRVaGeXoyjNRSpkZBJ3WyNzGxMIVWxlmiQhMiE-poAjx3luwIUIM5DSYPv40FC1ot3tbGlW-SPi0K6I6oh08wyMEY4gxVJyo_8Lgv1ngDdLtxbW44ILd-B7c7VAq223NahPWbHUfNjs_0LDX3bLqnQdQ71bM7SW_mLVDkKzlpGYIhhmCS1ajTzrrhj1ZXTLqjZ9Vy3rZMIqpzuzpvGK_MG2nQa6G5ZfMUGO9m8FirpbBTH2WzarmIZzcyPt-BOtVXdnHwJQ0SRkTUYhVghupuIlLmu21hUww1nsw6t-pLroN50S08UO7TIfoNq-qwYM3wyPzdr3HKuHtTlGD7DUZPTelBztX5Vbc-cqpfJDMzr9Tr10cafGV6297PE2DSaC_eLDV24Tu3Eyjh4_CAzb8iv6Bij5ZZVGVGhFiGEopoicrL3gBt9PjwwN9sH802YI77XIK6rR7CuuL86V9htBrkT93Bs_g9Ka_sL93vjkN |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lb9NAEB6VREJcEOUhTAvsgSKKZDVe27vrA0KFNEoJRBVQEfVibO9aimjtUCfQ_jT-HTP22ohWyq3X9XgPnt2ZbzyPD-BFgl4ykdHA5Wj-3CDkuZtKnrppEKYcg7dcZ9Sc_GkqxsfBh1k424A_bS8MlVW2NrE21LrM6B_5Hkeo4mEsIvdyWxVxNBy9Xfx0iUCKEq0tm0ZzQibm8jdGb9WbwyGqeofz0cHX92PXEgy4WeCppatM7mVSDPJQZyLD-CxUyjciTNGsJ0EuRKIRgBotUiOJkUsa4SdR4Gkf31Je5uO-t6AvKSjqQf_dwfToc5fCoEnvTaJUuUHEZzalWtPu4BouITRDxKFkpP5ziv86g_uk6YtrXqJ2faN7cNdiVrbfHLJN2DDFfdi0VqFir-zo6t0HUO4XrJ5SfjFvWiJZw1DNEBozhJqsRAt1Zls_WZkzqpSfF6tyVTHysPUloPWC_cIgntq6KpZeMk1l9nVHFqszG0yXZ8m8qB7C8Y188UfQK8rCPAamhI5ySbQhRgVcC8W1zKnT12QiQs_vwKD9pnFm550T7cZpXMc9RL55VQ0OvO5eWTTDPtYJ71hFdbLXZOKFzh3YvSq3Zs-Xtco7yeT8B1XeyTAOvvH4ZMjHY2_ixV8c2GrPRGyNThV3V8QB1j1Fa0EpoKQwqMoY8aLvCxGET9Zu8Bxu4-2KPx5OJ1twp5lUQWV329Bbnq_MU8Rhy_SZPfEMvt_0JfsLs2g-nw |
| 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=An+approximation+method+for+the+optimization+of+continuous+functions+of+n+variables+by+densifying+their+domains&rft.jtitle=Kybernetes&rft.au=Mora%2C+Gaspar&rft.au=Cherruault%2C+Yves&rft.date=1999-03-01&rft.issn=0368-492X&rft.volume=28&rft.issue=2&rft.spage=164&rft.epage=164&rft_id=info:doi/10.1108%2F03684929910258798&rft.externalDBID=NO_FULL_TEXT |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0368-492X&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0368-492X&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0368-492X&client=summon |