On finding new vertices and redundant constraints in cutting plane algorithms for global optimization
Identifieur interne : 003143 ( Main/Exploration ); précédent : 003142; suivant : 003144On finding new vertices and redundant constraints in cutting plane algorithms for global optimization
Auteurs : Reiner Horst [Allemagne] ; Jakob De Vries [Allemagne] ; Nguyen V. Thoai [Viêt Nam]Source :
- Operations Research Letters [ 0167-6377 ] ; 1988.
Abstract
Cutting plane algorithms belong to the basic tools for solving certain classes of global multiextremal optimization problems such as the global minimization of a concave function on a compact, convex set. The computationally most expensive part of these algorithms consists in the calculation of all new vertices of the polytope P created from a given polytope P (with known vertex set) by a cut. We first present a new procedure for solving this subproblem that allows to handle degeneracy and give a theoretical and numerical comparison with existing approaches. Then we show how redundant constraints can be eliminated by a criterion based on the known vertex set of a polytope.
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DOI: 10.1016/0167-6377(88)90071-5
Affiliations:
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Thoai</name><affiliation wicri:level="1"><country xml:lang="fr">Viêt Nam</country><wicri:regionArea>Institute of Mathematics, PO Box 631, Hanoi</wicri:regionArea><wicri:noRegion>Hanoi</wicri:noRegion></affiliation></author></analytic><monogr></monogr><series><title level="j">Operations Research Letters</title><title level="j" type="abbrev">OPERES</title><idno type="ISSN">0167-6377</idno><imprint><publisher>ELSEVIER</publisher><date type="published" when="1988">1988</date><biblScope unit="volume">7</biblScope><biblScope unit="issue">2</biblScope><biblScope unit="page" from="85">85</biblScope><biblScope unit="page" to="90">90</biblScope></imprint><idno type="ISSN">0167-6377</idno></series><idno type="istex">A5664C1BAFBEB551B6312DD4773CCD0B3E7D4C94</idno><idno type="DOI">10.1016/0167-6377(88)90071-5</idno><idno type="PII">0167-6377(88)90071-5</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0167-6377</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Cutting plane algorithms belong to the basic tools for solving certain classes of global multiextremal optimization problems such as the global minimization of a concave function on a compact, convex set. The computationally most expensive part of these algorithms consists in the calculation of all new vertices of the polytope P created from a given polytope P (with known vertex set) by a cut. We first present a new procedure for solving this subproblem that allows to handle degeneracy and give a theoretical and numerical comparison with existing approaches. Then we show how redundant constraints can be eliminated by a criterion based on the known vertex set of a polytope.</div></front></TEI><affiliations><list><country><li>Allemagne</li><li>Viêt Nam</li></country></list><tree><country name="Allemagne"><noRegion><name sortKey="Horst, Reiner" sort="Horst, Reiner" uniqKey="Horst R" first="Reiner" last="Horst">Reiner Horst</name></noRegion><name sortKey="De Vries, Jakob" sort="De Vries, Jakob" uniqKey="De Vries J" first="Jakob" last="De Vries">Jakob De Vries</name></country><country name="Viêt Nam"><noRegion><name sortKey="Thoai, Nguyen V" sort="Thoai, Nguyen V" uniqKey="Thoai N" first="Nguyen V" last="Thoai">Nguyen V. Thoai</name></noRegion></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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