Unbalanced optimal transport

Bernhard Schmitzer (TU München)

Abstract

Optimal transport induces a geometrically intuitive metric on the space
of probability measures and is a powerful tool in analysis and
mathematical modeling. With the evolution of efficient numerical methods
it is becoming increasingly popular in data analysis applications.
However, in many models the assumption that all measures have unit mass
and that mass is exactly preserved locally are too restrictive, for
instance in biochemical growth processes.

Hence, in recent years, "unbalanced" optimal transport problems, that
allow creation or annihilation of mass during transport, have received
increased attention.

In this talk we present several formulations for such problems,
efficient numerical methods and illustrate applications and advantages
of unbalanced metrics.