Seminar in Numerical Analysis: Rolf Krause (Università della Svizzera italiana)

Scales of Knowledge - Multilevel Minimization in Scientific Computing and Machine Learning

Non-convex minimization problems show up in manifold applications: non-linear elasticity, phase field models, fracture propagation, or the training of neural networks.

Traditional multilevel decompositions are the basic ingredient  of the most efficient class of solution methods for linear systems, i.e. of multigrid methods, which allow to solve certain classes of linear systems with optimal complexity. The transfer of these concepts to non-linear problems, however, is not straightforward, neither in terms of the design of the multilevel decomposition nor in terms of convergence properties. In this talk, we will discuss  multilevel decompositions for convex, non-convex and possibly non-smooth minimization problems. We will discuss in detail how  multilevel optimization methods can be constructed and analyzed and we will illustrate  the sometimes significant gain in performance, which can be achieved by multilevel minimization techniques. Examples from mechanics, geophysics, and machine learning will illustrate our discussion.

For further information about the seminar, please visit this webpage.

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