Isabel Haasler: Graph-structured multi-marginal optimal transport
In this pre-defense seminar, Isabel will present selected parts of her upcoming thesis.
Date of defence: Thursday, June 10, 2022, 14:00
Link to the thesis: http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-312138
Time: Tue 2022-05-31 13.00 - 14.00
Location: Seminar room 3721
Lecturer: Isabel Haasler
This thesis deals with a class of multi-marginal optimal transport problems, which we call graph-structured multi-marginal optimal transport.
Optimal transport has become an important tool in a wide range of applications, from image processing over machine learning to control theory. The classical optimal transport problem is to find a coupling between two distributions that minimizes a given associated cost. Multi-marginal optimal transport is a generalization of this problem to several distributions. This multi-marginal setting has lately received a lot of attention from theoretical and applied perspectives. In particular, the multi-marginal optimal transport has found applications in, e.g., imaging, finance, and physics. In many of these applications the problem has underlying structures.
The aim of this thesis is to introduce a framework for a special class of multi-marginal optimal transport problems, which have a structure that can be described by a graph. The included papers explore theoretical, computational, and practical aspects of the novel framework, e.g., connections to related areas, numerical algorithms for solving the problem, and applications in various fields.