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Quadratic convex reformulations for a class of complex quadratic programming problems

Author

Listed:
  • Cheng Lu

    (North China Electric Power University)

  • Gaojian Kang

    (North China Electric Power University)

  • Guangtai Qu

    (North China Electric Power University)

  • Zhibin Deng

    (University of Chinese Academy of Sciences
    University of Chinese Academy of Sciences)

Abstract

We investigate a class of complex quadratic programming problems characterized by unit-modulus and discrete argument constraints. This problem can be reformulated as a mixed-integer quadratic programming problem, which could be addressed using a commercial solver such as Gurobi. However, the solver’s efficiency is often unsatisfying if the problem formulation is inadequately designed. In this paper, we introduce several quadratic convex reformulations aimed at enhancing the solver’s performance. We extend the classical diagonal perturbation-based reformulation technique to this problem. Additionally, by leveraging the unique structure of the problem, we derive a new quadratic convex reformulation that provides a tighter continuous relaxation compared to the diagonal perturbation-based approach. The numerical tests on random instances and the unimodular code design problem demonstrate the superiority of the newly proposed reformulation.

Suggested Citation

  • Cheng Lu & Gaojian Kang & Guangtai Qu & Zhibin Deng, 2025. "Quadratic convex reformulations for a class of complex quadratic programming problems," Computational Optimization and Applications, Springer, vol. 91(1), pages 125-144, May.
    • Handle: RePEc:spr:coopap:v:91:y:2025:i:1:d:10.1007_s10589-025-00672-1
    DOI: 10.1007/s10589-025-00672-1
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    References listed on IDEAS

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    1. Alain Billionnet & Sourour Elloumi & Amélie Lambert, 2013. "An efficient compact quadratic convex reformulation for general integer quadratic programs," Computational Optimization and Applications, Springer, vol. 54(1), pages 141-162, January.
    2. M. Locatelli, 2024. "A new technique to derive tight convex underestimators (sometimes envelopes)," Computational Optimization and Applications, Springer, vol. 87(2), pages 475-499, March.
    3. Sourour Elloumi & Amélie Lambert & Arnaud Lazare, 2021. "Solving unconstrained 0-1 polynomial programs through quadratic convex reformulation," Journal of Global Optimization, Springer, vol. 80(2), pages 231-248, June.
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