Global optimization techniques for solving the general quadratic integer programming problem
Identifieur interne : 001677 ( PascalFrancis/Curation ); précédent : 001676; suivant : 001678Global optimization techniques for solving the general quadratic integer programming problem
Auteurs : N. Van Thoai [Allemagne]Source :
- Computational Optimization and Applications [ 0926-6003 ] ; 1998.
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- Pascal (Inist)
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Abstract
We consider the problem of minimizing a general quadratic function over a polytope in the n-dimensional space with integrality restrictions on all of the variables. (This class of problems contains, e.g., the quadratic 0-1 program as a special case.) A finite branch and bound algorithm is established, in which the branching procedure is the so-called integral rectangular partition', and the bound estimation is performed by solving a concave programming problem with a special structure. Three methods for solving this special concave program are proposed.
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Van Thoai</name><affiliation wicri:level="1"><inist:fA14 i1="01"><s1>Univ of Trier</s1><s2>Trier</s2><s3>DEU</s3><sZ>1 aut.</sZ></inist:fA14><country>Allemagne</country></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">INIST</idno><idno type="inist">98-0208641</idno><date when="1998">1998</date><idno type="stanalyst">PASCAL 98-0208641 EI</idno><idno type="RBID">Pascal:98-0208641</idno><idno type="wicri:Area/PascalFrancis/Corpus">001148</idno><idno type="wicri:Area/PascalFrancis/Curation">001677</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a">Global optimization techniques for solving the general quadratic integer programming problem</title><author><name sortKey="Van Thoai, N" sort="Van Thoai, N" uniqKey="Van Thoai N" first="N." last="Van Thoai">N. Van Thoai</name><affiliation wicri:level="1"><inist:fA14 i1="01"><s1>Univ of Trier</s1><s2>Trier</s2><s3>DEU</s3><sZ>1 aut.</sZ></inist:fA14><country>Allemagne</country></affiliation></author></analytic><series><title level="j" type="main">Computational Optimization and Applications</title><title level="j" type="abbreviated">Comput Optim Appl</title><idno type="ISSN">0926-6003</idno><imprint><date when="1998">1998</date></imprint></series></biblStruct></sourceDesc><seriesStmt><title level="j" type="main">Computational Optimization and Applications</title><title level="j" type="abbreviated">Comput Optim Appl</title><idno type="ISSN">0926-6003</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Algorithms</term><term>Branch and bound algorithms</term><term>Concave minimization</term><term>Global optimization</term><term>Integer programming</term><term>Optimization</term><term>Problem solving</term><term>Quadratic integer programming</term><term>Theory</term></keywords><keywords scheme="Pascal" xml:lang="fr"><term>Théorie</term><term>Optimisation</term><term>Résolution problème</term><term>Algorithme</term><term>Programmation en nombres entiers</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">We consider the problem of minimizing a general quadratic function over a polytope in the n-dimensional space with integrality restrictions on all of the variables. 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