On Tikhonov's Reciprocity Principle and Optimality Conditions in d.c. Optimization
Identifieur interne : 000769 ( Istex/Corpus ); précédent : 000768; suivant : 000770On Tikhonov's Reciprocity Principle and Optimality Conditions in d.c. Optimization
Auteurs : Nguyen V. ThoaiSource :
- Journal of Mathematical Analysis and Applications [ 0022-247X ] ; 1998.
English descriptors
Abstract
The basic idea of the reciprocity principle of Tikhonov is to construct, from a given problem, a reciprocal problem that has the same solution set as the original problem and some special structure one can employ to investigate theoretical properties as well as to develop solution methods. In this note, we prove the reciprocity principle for a pair of nonconvex optimization problems, from which some optimality conditions for d.c. optimization can be derived immediately.
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DOI: 10.1006/jmaa.1998.6040
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Thoai</name></json:item></author><host><volume>5</volume><pages><last>348</last><first>333</first></pages><author></author><title>J. Global Optim.</title></host><title>Constraint decomposition algorithms in global optimization</title></json:item><json:item><host><author></author><title>Global Optimization: Deterministic Approaches</title></host></json:item><json:item><author><json:item><name>J.B. Hiriart-Urruty</name></json:item></author><host><pages><last>239</last><first>219</first></pages><author></author><title>Nonsmooth Optimization and Related Topics</title></host><title>From convex optimization to nonconvex optimization. Part 1: Necessary and sufficient conditions for global optimality</title></json:item><json:item><author><json:item><name>J.B. Hiriart-Urruty</name></json:item></author><host><pages><last>26</last><first>1</first></pages><author></author><title>Handbook of Global Optimization</title></host><title>Condition for global optimality</title></json:item><json:item><author><json:item><name>N.V. Thoai</name></json:item></author><host><volume>50</volume><pages><last>253</last><first>241</first></pages><author></author><title>Computing</title></host><title>Canonical dc-programming techniques for solving a convex program with an additional constraint of multiplicative type</title></json:item><json:item><author><json:item><name>A.N. Tikhonov</name></json:item></author><host><volume>22</volume><pages><last>103</last><first>100</first></pages><author></author><title>Sov. Math.</title></host><title>On a reciprocity principle</title></json:item><json:item><author><json:item><name>H. Tuy</name></json:item></author><host><volume>52</volume><pages><last>486</last><first>463</first></pages><author></author><title>J. Optim. 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Optimization</ce:title><ce:author-group><ce:author><ce:given-name>Nguyen V</ce:given-name><ce:surname>Thoai</ce:surname><ce:cross-ref refid="AY986040FNAST">*<ce:footnote id="AY986040FNAST"><ce:label>*</ce:label><ce:note-para>E-mail address:thoai@uni-trier.de.</ce:note-para></ce:footnote></ce:cross-ref></ce:author><ce:affiliation><ce:textfn>Department of Mathematics, University of Trier, D-54286, Trier, Germany</ce:textfn></ce:affiliation></ce:author-group><ce:date-received day="28" month="1" year="1998"></ce:date-received><ce:abstract><ce:section-title>Abstract</ce:section-title><ce:abstract-sec><ce:simple-para>The basic idea of the reciprocity principle of Tikhonov is to construct, from a given problem, a reciprocal problem that has the same solution set as the original problem and some special structure one can employ to investigate theoretical properties as well as to develop solution methods. In this note, we prove the reciprocity principle for a pair of nonconvex optimization problems, from which some optimality conditions for d.c. optimization can be derived immediately.</ce:simple-para></ce:abstract-sec></ce:abstract><ce:keywords><ce:section-title>Keywords</ce:section-title><ce:keyword><ce:text>nonlinear optimization</ce:text></ce:keyword><ce:keyword><ce:text>reciprocity principle</ce:text></ce:keyword><ce:keyword><ce:text>d.c. optimization</ce:text></ce:keyword><ce:keyword><ce:text>optimality conditions</ce:text></ce:keyword></ce:keywords></head></converted-article></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>On Tikhonov's Reciprocity Principle and Optimality Conditions in d.c. Optimization</title></titleInfo><titleInfo type="alternative" lang="en" contentType="CDATA"><title>On Tikhonov's Reciprocity Principle and Optimality Conditions in d.c. Optimization</title></titleInfo><name type="personal"><namePart type="given">Nguyen V</namePart><namePart type="family">Thoai</namePart><affiliation>Department of Mathematics, University of Trier, D-54286, Trier, Germany</affiliation><description>E-mail address:thoai@uni-trier.de.</description><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="brief-communication" displayLabel="Short communication"></genre><originInfo><publisher>ELSEVIER</publisher><dateIssued encoding="w3cdtf">1998</dateIssued><copyrightDate encoding="w3cdtf">1998</copyrightDate></originInfo><language><languageTerm type="code" authority="iso639-2b">eng</languageTerm><languageTerm type="code" authority="rfc3066">en</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType></physicalDescription><abstract lang="en">The basic idea of the reciprocity principle of Tikhonov is to construct, from a given problem, a reciprocal problem that has the same solution set as the original problem and some special structure one can employ to investigate theoretical properties as well as to develop solution methods. In this note, we prove the reciprocity principle for a pair of nonconvex optimization problems, from which some optimality conditions for d.c. optimization can be derived immediately.</abstract><note>Submitted by George, Leitmann</note><note type="content">Section title: Note</note><subject lang="en"><genre>Keywords</genre><topic>nonlinear optimization</topic><topic>reciprocity principle</topic><topic>d.c. optimization</topic><topic>optimality conditions</topic></subject><relatedItem type="host"><titleInfo><title>Journal of Mathematical Analysis and Applications</title></titleInfo><titleInfo type="abbreviated"><title>YJMAA</title></titleInfo><genre type="journal">journal</genre><originInfo><dateIssued encoding="w3cdtf">19980915</dateIssued></originInfo><identifier type="ISSN">0022-247X</identifier><identifier type="PII">S0022-247X(00)X0063-7</identifier><part><date>19980915</date><detail type="volume"><number>225</number><caption>vol.</caption></detail><detail type="issue"><number>2</number><caption>no.</caption></detail><extent unit="issue pages"><start>359</start><end>686</end></extent><extent unit="pages"><start>673</start><end>678</end></extent></part></relatedItem><identifier type="istex">52A4B97C2243E595217D4891040A8784188CA227</identifier><identifier type="DOI">10.1006/jmaa.1998.6040</identifier><identifier type="PII">S0022-247X(98)96040-1</identifier><accessCondition type="use and reproduction" contentType="copyright">©1998 Academic Press</accessCondition><recordInfo><recordContentSource>ELSEVIER</recordContentSource><recordOrigin>Academic Press, ©1998</recordOrigin></recordInfo></mods></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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