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Maximization of a Convex Quadratic Form on a Polytope: Factorization and the Chebyshev Norm Bounds
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SYSNO ASEP 0507646 Document Type C - Proceedings Paper (int. conf.) R&D Document Type Conference Paper Title Maximization of a Convex Quadratic Form on a Polytope: Factorization and the Chebyshev Norm Bounds Author(s) Hladík, M. (CZ)
Hartman, David (UIVT-O) RID, SAI, ORCIDSource Title Optimization of Complex Systems: Theory, Models, Algorithms and Applications. - Cham : Springer, 2020 / Le Thi H. A. ; Minh Le H. ; Pham Dinh T. - ISBN 978-3-030-21802-7 Pages s. 119-127 Number of pages 9 s. Publication form Print - P Action WCGO 2019: World Congress on Global Optimization /6./ Event date 08.07.2019 - 10.07.2019 VEvent location Metz Country FR - France Event type WRD Language eng - English Country CH - Switzerland Keywords Convex quadratic form ; Relaxation ; NP-hardness ; Interval computation Subject RIV BA - General Mathematics OECD category Pure mathematics Institutional support UIVT-O - RVO:67985807 EID SCOPUS 85068382414 DOI 10.1007/978-3-030-21803-4_12 Annotation Maximization of a convex quadratic form on a convex polyhedral set is an NP-hard problem. We focus on computing an upper bound based on a factorization of the quadratic form matrix and employment of the maximum vector norm. Effectivity of this approach depends on the factorization used. We discuss several choices as well as iterative methods to improve performance of a particular factorization. We carried out numerical experiments to compare various alternatives and to compare our approach with other standard approaches, including McCormick envelopes. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2021
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