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Mathematics > Optimization and Control

arXiv:2211.07287 (math)
[Submitted on 14 Nov 2022]

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

Authors:Sebastian Hillbrecht, Paul Manns, Christian Meyer
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Abstract: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.
Comments: 21 pages, 0 figures
Subjects: Optimization and Control (math.OC)
MSC classes: 49Q22, 90C08, 49J45
Cite as: arXiv:2211.07287 [math.OC]
  (or arXiv:2211.07287v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2211.07287

Submission history

From: Sebastian Hillbrecht [view email]
[v1] Mon, 14 Nov 2022 11:33:13 UTC (33 KB)
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