基于体积比较的double-McCormick松弛的实验验证
Experimental validation of volume-based comparison for double-McCormick relaxations
摘要：
体积是比较非凸集的多面体松弛的自然几何度量。Speakman和Lee给出了用于比较三线性单项式松弛的体积公式，量化了各种自然松弛的强度。他们的工作是由空间分支定界算法的因式分解的平行规划公式。他们从数学上分析了一个重要的选择，每当三个或更多的术语在公式中相乘时，都需要做出这个选择。我们通过实验证实了他们的主要结果的全局优化的实践的相关性，通过将其应用到困难的箱立方问题（boxcup）。在这样做的时候，我们发现，使用他们的体积公式，我们可以准确地预测的质量的放松boxcups的基础上（盒）参数定义的可行域。
英文摘要：
Volume is a natural geometric measure for comparing polyhedral relaxations of non-convex sets. Speakman and Lee gave volume formulae for comparing relaxations of trilinear monomials, quantifying the strength of various natural relaxations. Their work was motivated by the spatial branch-and-bound algorithm for factorable mathematical-programming formulations. They mathematically analyzed an important choice that needs to be made whenever three or more terms are multiplied in a formulation. We experimentally substantiate the relevance of their main results to the practice of global optimization, by applying it to difficult box cubic problems (boxcup). In doing so, we find that, using their volume formulae, we can accurately predict the quality of a relaxation for boxcups based on the (box) parameters defining the feasible region.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
