Testing copositivity with the help of difference-of-convex optimization
Autor: | Jean-Baptiste Hiriart-Urruty, Mirjam Dür |
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Přispěvatelé: | Department of Mathematics [Trier], Universität Trier, Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Trier University, Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS) |
Rok vydání: | 2013 |
Předmět: |
Mathematical optimization
021103 operations research Fenchel's duality theorem General Mathematics 010102 general mathematics Mathematics::Optimization and Control 0211 other engineering and technologies Duality (optimization) 02 engineering and technology 01 natural sciences Orthant Maxima and minima 90C26 (15A63 46N10) Convex optimization Symmetric matrix [MATH]Mathematics [math] 0101 mathematics Convex function Subgradient method ComputingMilieux_MISCELLANEOUS Software Mathematics |
Zdroj: | Mathematical Programming Mathematical Programming, Springer Verlag, 2013, 140 (1), p. 31-43. ⟨10.1007/s10107-012-0625-9⟩ Mathematical Programming, 2013, 140, pp.31-43. ⟨10.1007/s10107-012-0625-9⟩ |
ISSN: | 1436-4646 0025-5610 |
DOI: | 10.1007/s10107-012-0625-9 |
Popis: | International audience; We consider the problem of minimizing an indefinite quadratic form over the nonnegative orthant, or equivalently, the problem of deciding whether a symmetric matrix is copositive. We formulate the problem as a difference of convex functions problem. Using conjugate duality, we show that there is a one-to-one correspondence between their respective critical points and minima. We then apply a subgradient algorithm to approximate those critical points and obtain an efficient heuristic to verify non-copositivity of a matrix. |
Databáze: | OpenAIRE |
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