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Data-driven nonsmoo...
Data-driven nonsmooth optimization
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- Banert, Sebastian (author)
- KTH,Matematik (Avd.)
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- Ringh, Axel (author)
- KTH,Optimeringslära och systemteori
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- Adler, Jonas (author)
- KTH,Matematik (Avd.),Elekta, Box 7593, S-10393 Stockholm, Sweden.
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- Karlsson, Johan (author)
- KTH,Optimeringslära och systemteori
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- Öktem, Ozan, 1969- (author)
- KTH,Matematik (Avd.)
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KTH Matematik (Avd) (creator_code:org_t)
- Society for Industrial & Applied Mathematics (SIAM), 2020
- 2020
- English.
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In: SIAM Journal on Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 1052-6234 .- 1095-7189. ; 30:1, s. 102-131
- Related links:
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https://urn.kb.se/re...
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https://doi.org/10.1...
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Abstract
Subject headings
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- In this work, we consider methods for solving large-scale optimization problems with a possibly nonsmooth objective function. The key idea is to first parametrize a class of optimization methods using a generic iterative scheme involving only linear operations and applications of proximal operators. This scheme contains some modern primal-dual first-order algorithms like the Douglas-Rachford and hybrid gradient methods as special cases. Moreover, we show weak convergence of the iterates to an optimal point for a new method which also belongs to this class. Next, we interpret the generic scheme as a neural network and use unsupervised training to learn the best set of parameters for a specific class of objective functions while imposing a fixed number of iterations. In contrast to other approaches of "learning to optimize," we present an approach which learns parameters only in the set of convergent schemes. Finally, we illustrate the approach on optimization problems arising in tomographic reconstruction and image deconvolution, and train optimization algorithms for optimal performance given a fixed number of iterations.
Subject headings
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Keyword
- convex optimization
- proximal algorithms
- monotone operators
- machine learning
- inverse problems
- computerized tomography
Publication and Content Type
- ref (subject category)
- art (subject category)
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