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World Congress on Global Optimization

WCGO 2019: Optimization of Complex Systems: Theory, Models, Algorithms and Applications pp 119–127Cite as

Maximization of a Convex Quadratic Form on a Polytope: Factorization and the Chebyshev Norm Bounds

Part of the Advances in Intelligent Systems and Computing book series (AISC,volume 991)

Abstract

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.

Keywords

  • Convex quadratic form
  • Relaxation
  • NP-hardness
  • Interval computation

Supported by the Czech Science Foundation Grant P403-18-04735S.

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Author information

Authors and Affiliations

  1. Faculty of Mathematics and Physics, Department of Applied Mathematics, Charles University, Malostranské nám. 25, 11800, Prague, Czech Republic

    Milan Hladík

  2. Computer Science Institute, Charles University, Malostranské nám. 25, 11800, Prague, Czech Republic

    David Hartman

  3. Institute of Computer Science of the Czech Academy of Sciences, Prague, Czech Republic

    David Hartman

Authors
  1. Milan Hladík
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  2. David Hartman
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Corresponding author

Correspondence to Milan Hladík .

Editor information

Editors and Affiliations

  1. Computer science and Applications Department, LGIPM, University of Lorraine, Metz Cedex 03, France

    Prof. Hoai An Le Thi

  2. Computer Science and Applications Department, LGIPM, University of Lorraine, Metz Cedex 03, France

    Assoc. Prof. Hoai Minh Le

  3. Laboratory of Mathematics, National Institute for Applied Sciences (INSA)-Rouen Normadie, Saint-Étienne-du-Rouvray Cedex, France

    Prof. Tao Pham Dinh

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Hladík, M., Hartman, D. (2020). Maximization of a Convex Quadratic Form on a Polytope: Factorization and the Chebyshev Norm Bounds. In: Le Thi, H., Le, H., Pham Dinh, T. (eds) Optimization of Complex Systems: Theory, Models, Algorithms and Applications. WCGO 2019. Advances in Intelligent Systems and Computing, vol 991. Springer, Cham. https://doi.org/10.1007/978-3-030-21803-4_12

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