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

  • Milan HladíkEmail author
  • David Hartman
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 991)


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.


Convex quadratic form Relaxation NP-hardness Interval computation 


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Authors and Affiliations

  1. 1.Faculty of Mathematics and Physics, Department of Applied MathematicsCharles UniversityPragueCzech Republic
  2. 2.Computer Science Institute, Charles UniversityPragueCzech Republic
  3. 3.Institute of Computer Science of the Czech Academy of SciencesPragueCzech Republic

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