论文标题
karush-kuhn-tucker和价值功能重新恢复的理论和数值比较
Theoretical and numerical comparison of the Karush-Kuhn-Tucker and value function reformulations in bilevel optimization
论文作者
论文摘要
Karush-kuhn-tucker和值函数（确切的较低价值函数）是重新制定是双层优化问题的最常见的单层转换。到目前为止，这些重新构造已经独立研究，或者是作为关节优化问题，以尝试利用每个模型的最佳属性。据我们所知，在现有文献中尚未比较这些重新制定。本文是确定其中一种重新制定的首次尝试，是否最好是解决特定类别的乐观双层优化问题。我们设计了一个比较框架，考虑到这些重新纠正的理论特性，该框架似乎很公平。这项工作表明，尽管从理论的角度来看，这些模型似乎都没有特别主导另一个模型，但价值函数重新制定似乎在数值上优于Karush-Kuhn-tucker在牛顿型算法上的重新印象。此处的计算实验主要基于双重优化库（Bolib）的测试问题。
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).
