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ALOP Colloquium with Daniel Walter
16. November 2023 / 16:00 - 17:00
On Thursday, November 16, 2023 at 16:00 c.t. Prof. Dr. Daniel Walter, HU Berlin, will speak at the ALOP Colloquium about his recent work.
If you would like to participate via Zoom, please click here.
Efficient minimization in spaces of measures: Numerical methods and applications
Abstract:
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.
Please join us at 16:00 c.t. in HS 9.