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DTSTART:19810329T020000
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BEGIN:VEVENT
UID:news1257@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20211025T121842
DTSTART;TZID=Europe/Zurich:20211112T110000
SUMMARY:Seminar in Numerical Analysis: Rolf Krause (Università della Svizz
 era italiana)
DESCRIPTION:Non-convex minimization problems show up in manifold applicatio
 ns: non-linear elasticity\, phase field models\, fracture propagation\, or
  the training of neural networks.  Traditional multilevel decompositions a
 re the basic ingredient  of the most efficient class of solution methods 
 for linear systems\, i.e. of multigrid methods\, which allow to solve cert
 ain classes of linear systems with optimal complexity. The transfer of the
 se concepts to non-linear problems\, however\, is not straightforward\, ne
 ither in terms of the design of the multilevel decomposition nor in terms 
 of convergence properties. In this talk\, we will discuss  multilevel dec
 ompositions for convex\, non-convex and possibly non-smooth minimization p
 roblems. We will discuss in detail how  multilevel optimization methods c
 an be constructed and analyzed and we will illustrate  the sometimes sign
 ificant gain in performance\, which can be achieved by multilevel minimiza
 tion techniques. Examples from mechanics\, geophysics\, and machine learni
 ng will illustrate our discussion.\\r\\nFor further information about the 
 seminar\, please visit this webpage [t3://page?uid=1115].
X-ALT-DESC:<p>Non-convex minimization problems show up in manifold applicat
 ions: non-linear elasticity\, phase field models\, fracture propagation\, 
 or the training of neural networks.<br /> <br /> Traditional multilevel de
 compositions are the basic ingredient &nbsp\;of the most efficient class o
 f 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 s
 traightforward\, neither in terms of the design of the multilevel decompos
 ition nor in terms of convergence properties. In this talk\, we will discu
 ss &nbsp\;multilevel decompositions for convex\, non-convex and possibly n
 on-smooth minimization problems. We will discuss in detail how &nbsp\;mult
 ilevel optimization methods can be constructed and analyzed and we will il
 lustrate &nbsp\;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.</p>\n
 <p>For further information about the seminar\, please visit this <a href="
 t3://page?uid=1115" title="Opens internal link in current window">webpage<
 /a>.</p>
DTEND;TZID=Europe/Zurich:20211112T120000
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