论文标题
Kantorovich问题及其二次正则化第II部分的二重性优化：收敛分析
Bilevel Optimization of the Kantorovich Problem and its Quadratic Regularization Part II: Convergence Analysis
论文作者
论文摘要
本文关注的是一个受坎托洛维奇最佳运输问题约束的优化问题。可以将这个双重优化问题重新制定为数学问题，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二部分。尽管在第一部分中显示了对二聚体坎托维奇问题及其正则化对应物的最佳解决方案的存在，但本文介绍了（弱*）解决方案与正则二聚体问题的（弱*）收敛到原始的bilevel kantorovich问题的解决方案。
This paper is concerned with an optimization problem that is constrained by the Kantorovich optimal transportation problem. This bilevel optimization problem 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 second part in a series of three papers. While the existence of optimal solutions to both the bilevel Kantorovich problem and its regularized counterpart were shown in the first part, this paper deals with the (weak-*) convergence of solutions to the regularized bilevel problem to solutions of the original bilevel Kantorovich problem.
