This talk will be held in a hybrid format, both in person at Open Space* of RIKEN AIP (Nihonbashi office) and online by Zoom. Open Space: *only available to AIP researchers.
DATE, TIME & LOCATION
Wednesday, February 18th, 10:00 - 11:00, RIKEN AIP Nihombashi Office, Open Space
TITLE
Nonsmooth Optimization on Riemannian Manifolds
ABSTRACT
In many applications nonlinear data is measured, for example when considering unit vectors, rotations, or (bases of) subspaces of a vector space. Modelling this on a Riemannian manifold allows to both reduce the dimension of the data stored as well as focusing on geometric properties of the measurement space compared to constraining a total space the data is represented in. In optimization this yields unconstrained optimization algorithms, where we obtain that every iterate is a feasible point, but we have to take the geometry of the optimization domain into consideration. In this talk we present recent developments in nonsmooth optimization on manifolds. Besides a short historical overview the main algorithms will be so-called splitting methods, where the objective function can be split into several parts, where some summand need to fulfil different properties. Numerical examples will be given as well, illustrating that the obtained algorithms are both performant and easy to use.
BIO
Ronny Bergmann is Associate Professor at the Department of Mathematical Sciences since March 2021. He was a researcher and deputy head Arbeitsgruppe Numerik partieller Differentialgleichungen, Technische Universität Chemnitz, which he joined in April 2018. Previously he worked within the Image Processing Group, Technische Universität Kaiserslautern, where he finished his habilitation beginning of 2018. Prior to that he was a doctoral researcher and teaching assistant at the Institut für Mathematik, Universität zu Lübeck, working together with his PhD supervisor Jürgen Prestin. His website is https://ronnybergmann.net/
