As part of the colloquium of the Research Training Group Algorithmic Optimization will take place on

Thursday, November 16, 2023
16:00 c.t.
Lecture hall 9

the following lecture will take place:

Efficient minimization in spaces of measures: Numerical methods and applications

Prof. Dr. Daniel Walter, HU Berlin

Minimization problems in spaces of (vector) measures naturally emerge in a variety of challenging settings including e.g. inverse problems in acoustics and seismology, micoscropy, optimal sensor placement as well as the training of shallow neural networks.

In this talk, we discuss several of these applications, both from a theoretical and numerical perspective, highlighting the difficulties posed by the (typical) nonsmoothness of the arising optimization problems as well as the lack of "nice" topological properties in the space of (vector) measures. Different practical solution ansatzes are discussed with a particular focus on generalized conditional gradient methods.

Finally, we further underline the practical relevance of "sparse" minimization problems by showing that a huge class of nonsmooth problems can be equivalently rewritten as an optimization problem over  measures on a compact metric space using arguments from convex representation theory. From a practical perspective, this unification allows the derivation and analysis of an efficient general purpose solution algorithm by "lifting" arguments from the vector measure setting.