Siegel der Universität Augsburg

Universität Augsburg
Institut für Mathematik

Siegel der Universität Augsburg

 

Analysis-Seminar Augsburg-München

 

Professor Dr. D. Russell Luke
Universität Göttingen

 
spricht am
 
Donnerstag, 12. Januar 2023
 
um
 
17:15 Uhr
 
im
 
TUM, Boltzmann-3, Garching, Raum 03.08.011, Etage 3
 
über das Thema:
 

»Convergence in Distribution of Randomized Algorithms: The Case of Partially Separable Optimization«

Abstract:
We present a Markov-chain analysis of blockwise-stochastic algorithms for solving partially block-separable optimization problems. Our main contributions to the extensive literature on these methods are statements about the Markov operators and distributions behind the iterates of stochastic algorithms, and in particular the regularity of Markov operators and rates of convergence of the distributions of the corresponding Markov chains. This provides a detailed characterization of the moments of the sequences beyond just the expected behavior. This also serves as a case study of how randomization restores favorable properties to algorithms that iterations of only partial information destroys. We demonstrate this on stochastic blockwise implementations of the forward-backward and Douglas- Rachford algorithms for nonconvex (and, as a special case, convex), nonsmooth optimization.

 

Hierzu ergeht herzliche Einladung.



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