论文标题
Kantorovich问题及其二次正则化第I部分的二重性优化：存在结果
Bilevel Optimization of the Kantorovich Problem and its Quadratic Regularization Part I: Existence Results
论文作者
论文摘要
本文关注的是由坎托洛维奇最佳运输问题控制的优化问题。这引起了一个双重优化问题，可以将其重新归类为数学问题，并在常规Borel措施的空间中具有互补性约束。由于互补关系引起的非平滑度，这种类型的问题通常是正规化的。在这里，我们应用了Kantorovich问题的二次正规化。如标题所示，这是一系列三篇论文的第一部分。它解决了二聚体坎托维奇问题及其二次正则化的最佳解决方案，而第二部分和III则致力于消失正则化的收敛分析。
This paper is concerned with an optimization problem governed by the Kantorovich optimal transportation problem. This gives rise to a bilevel optimization problem, which can be reformulated as a mathematical problem with complementarity constraints in the space of regular Borel measures. Because of the non-smoothness induced by the complementarity relations, problems of this type are frequently regularized. Here we apply a quadratic regularization of the Kantorovich problem. As the title indicates, this is the first part in a series of three papers. It addresses the existence of optimal solutions to the bilevel Kantorovich problem and its quadratic regularization, whereas part II and III are dedicated to the convergence analysis for vanishing regularization.
