Convergence in Distribution of Randomized Algorithms: The Case of Partially Separable Optimization
2023-02-23 | preprint. A publication with affiliation to the University of Göttingen.
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- Authors
- Luke, Russell ; Luke, D. Russell
- 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.
- Issue Date
- 23-February-2023
- Project
- SFB 1456: Mathematik des Experiments: Die Herausforderung indirekter Messungen in den Naturwissenschaften
SFB 1456 | Cluster C | C02: Stochastic computed tomography: theory and algorithms for single-shot X-FEL imaging - Organization
- Institut für Numerische und Angewandte Mathematik
- Working Group
- RG Luke (Continuous Optimization, Variational Analysis and Inverse Problems)
- Extent
- 23
- Language
- English
- Subject(s)
- Nonconvex; optimization; Markov chain; random function iteration; convergence rates