Bilevel Optimization of the Kantorovich Problem and its Quadratic Regularization Part II: Convergence Analysis

Autor:	Hillbrecht, Sebastian, Manns, Paul, Meyer, Christian
Rok vydání:	2022
Předmět:	Mathematics - Optimization and Control 49Q22 90C08 49J45
Druh dokumentu:	Working Paper
Popis:	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. Comment: 21 pages, 0 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2211.07287 Zobrazit plný text záznamu View this record from Arxiv