论文标题
二元性理论用于乐观的双重优化
Duality theory for optimistic bilevel optimization
论文作者
论文摘要
在本文中，我们利用了二聚体优化问题的所谓价值功能重新重新制定，以开发问题的双重性结果。我们的方法以Fenchel-Lagrange型二元性为基础，以为双光线优化问题建立合适的结果。首先，我们概述了一些标准二元性结果，以表明它们不适用于我们的问题。其次，通过部分平静的概念，我们建立了弱和强的二元性结果。特别是，在某些适当的条件下，研究了这种类型的问题的Lagrange，Fenchel-Lagrange和Toland-Fenchel-lagrange二元性概念。第三，基于对二线计划的某些正规化的使用，我们建立了足够的条件，以确保在普通的Slater型条件下没有凸度假设并且没有部分平静条件的情况下，确保了强大的二元性结果。最后，在没有滑底条件的情况下，为与几何约束的双重优化问题构建了强双重性结果。
In this paper, we exploit the so-called value function reformulation of the bilevel optimization problem to develop duality results for the problem. Our approach builds on Fenchel-Lagrange-type duality to establish suitable results for the bilevel optimization problem. First, we overview some standard duality results to show that they are not applicable to our problem. Secondly, via the concept of partial calmness, we establish weak and strong duality results. In particular, Lagrange, Fenchel-Lagrange, and Toland-Fenchel- Lagrange duality concepts are investigated for this type of problems under some suitable conditions. Thirdly, based on the use of some regularization of our bilevel program, we establish sufficient conditions ensuring strong duality results under a generalized Slater-type condition without convexity assumptions and without the partial calmness condition. Finally, without the Slater condition, a strong duality result is constructed for the bilevel optimization problem with geometric constraint.
