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<p>Domain reduction techniques are at the core of any global optimization solver for NLP or MINLP problems. In this paper, we delve into several of these techniques and assess the impact they may have in the performance of an RLT-based algorithm for polynomial optimization problems. These techniques include (i)&#xa0;the use of (nonlinear) conic relaxations for optimality-based bound tightening, (ii)&#xa0;the use of Lagrangian dual information to enhance feasibility-based bound tightening, and (iii)&#xa0;different strategies for branching point selection. One of this paper’s main contributions is providing insights into the relative impact of these techniques with respect to each other, which we hope will guide the efforts to develop and implement this type of enhancements in other solvers. We also explore how a solver equipped with these domain reduction enhancements can further improve its performance by using machine learning to better choose the best domain reduction approach to use on a given instance.</p>

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Impact of domain reduction techniques in polynomial optimization: a computational study

  • 期刊论文

  • 发表日期：

    2025年9月26日

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  • Ignacio Gómez-Casares,
  • Brais González-Rodríguez,
  • Julio González-Díaz,
  • Pablo Rodríguez-Fernández

摘要

Domain reduction techniques are at the core of any global optimization solver for NLP or MINLP problems. In this paper, we delve into several of these techniques and assess the impact they may have in the performance of an RLT-based algorithm for polynomial optimization problems. These techniques include (i) the use of (nonlinear) conic relaxations for optimality-based bound tightening, (ii) the use of Lagrangian dual information to enhance feasibility-based bound tightening, and (iii) different strategies for branching point selection. One of this paper’s main contributions is providing insights into the relative impact of these techniques with respect to each other, which we hope will guide the efforts to develop and implement this type of enhancements in other solvers. We also explore how a solver equipped with these domain reduction enhancements can further improve its performance by using machine learning to better choose the best domain reduction approach to use on a given instance.