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On monotonicity and search strategies in face-based copositivity detection algorithms

Author

Listed:
  • B. G.-Tóth

    (University of Szeged)

  • E. M. T. Hendrix

    (Universidad de Málaga
    Wageningen University)

  • L. G. Casado

    (Universidad de Almería, (ceiA3))

Abstract

Over the last decades, algorithms have been developed for checking copositivity of a matrix. Methods are based on several principles, such as spatial branch and bound, transformation to Mixed Integer Programming, implicit enumeration of KKT points or face-based search. Our research question focuses on exploiting the mathematical properties of the relative interior minima of the standard quadratic program (StQP) and monotonicity. We derive several theoretical properties related to convexity and monotonicity of the standard quadratic function over faces of the standard simplex. We illustrate with numerical instances up to 28 dimensions the use of monotonicity in face-based algorithms. The question is what traversal through the face graph of the standard simplex is more appropriate for which matrix instance; top down or bottom up approaches. This depends on the level of the face graph where the minimum of StQP can be found, which is related to the density of the so-called convexity graph.

Suggested Citation

  • B. G.-Tóth & E. M. T. Hendrix & L. G. Casado, 2022. "On monotonicity and search strategies in face-based copositivity detection algorithms," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 30(3), pages 1071-1092, September.
    • Handle: RePEc:spr:cejnor:v:30:y:2022:i:3:d:10.1007_s10100-021-00737-6
    DOI: 10.1007/s10100-021-00737-6
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