The Karush–Kuhn–Tucker and value function (lower-level value function, to be precise) reformulations are the most common single-level transformations of the bilevel optimization problem. So far, these reformulations have either been studied independently or as a joint optimization problem in an attempt to take advantage of the best properties from each model. To the best of our knowledge, these reformulations have not yet been compared in the existing literature. This paper is a first attempt towards establishing whether one of these reformulations is best at solving a given class of the optimistic bilevel optimization problem. We design a comparison framework, which seems fair, considering the theoretical properties of these reformulations. This work reveals that although none of the models seems to particularly dominate the other from the theoretical point of view, the value function reformulation seems to numerically outperform the Karush–Kuhn–Tucker reformulation on a Newton-type algorithm. The computational experiments here are mostly based on test problems from the Bilevel Optimization LIBrary (BOLIB).

Karush–Kuhn–Tucker和值函数（较低级别的值函数，确切地说，重新定义是双层优化问题中最常见的单级转换。到目前为止，这些重新公式已被单独研究或作为联合优化问题进行了研究，试图利用每个模型的最佳性能。据我们所知，这些重新制定尚未在现有文献中进行比较。本文是首次尝试确定这些重构之一是否最适合解决给定类别的乐观双层优化问题。考虑到这些重新制定的理论性质，我们设计了一个比较合理的比较框架。这项工作表明，尽管从理论上讲，似乎没有一个模型能特别主导另一个模型，在牛顿型算法上，值函数的重构在数值上优于Karush-Kuhn-Tucker的重构。这里的计算实验主要基于双级优化库（BOLIB）的测试问题。