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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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Correspondence to Milan Hladík .

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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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