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Degree reduction techniques for polynomial optimization problems

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  • González-Rodríguez, Brais
  • Naoum-Sawaya, Joe

Abstract

This paper presents a new approach to quadrify a polynomial programming problem, i.e. reduce the polynomial program to a quadratic program, before solving it. The proposed approach, QUAD-RLT, exploits the Reformulation-Linearization Technique (RLT) structure to obtain smaller relaxations that can be solved faster and still provide high quality bounds. QUAD-RLT is compared to other quadrification techniques that have been previously discussed in the literature. The paper presents theoretical as well as computational results showing the advantage of QUAD-RLT compared to other quadrification techniques. Furthermore, rather than quadrifying a polynomial program, QUAD-RLT is generalized to reduce the degree of the polynomial to any degree. Computational results show that reducing the degree of the polynomial to a degree that is higher than two provides computational advantages in certain cases compared to fully quadrifying the problem. Finally, QUAD-RLT along with other quadrification/degree reduction schemes are implemented and made available in the freely available software RAPOSa.

Suggested Citation

  • González-Rodríguez, Brais & Naoum-Sawaya, Joe, 2025. "Degree reduction techniques for polynomial optimization problems," European Journal of Operational Research, Elsevier, vol. 322(2), pages 401-413.
    • Handle: RePEc:eee:ejores:v:322:y:2025:i:2:p:401-413
    DOI: 10.1016/j.ejor.2024.12.021
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