3 papers
math.OC2024
Bilevel Optimization of the Kantorovich Problem and its Quadratic Regularization Part III: The Finite-Dimensional Case
Sebastian Hillbrecht
As the title suggests, this is the third paper in a series addressing bilevel optimization problems that are governed by the Kantorovich problem of optimal transport. These tasks c…
math.OC2022
Bilevel Optimization of the Kantorovich Problem and its Quadratic Regularization Part II: Convergence Analysis
Sebastian Hillbrecht, Paul Manns, Christian Meyer
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…
math.OC2022
Bilevel Optimization of the Kantorovich Problem and its Quadratic Regularization Part I: Existence Results
Sebastian Hillbrecht, Christian Meyer
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 ref…