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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

Language: English

Lecturer: Isabel Haasler

Abstract

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.