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Forward-reflected-b...
Forward-reflected-backward method with variance reduction
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- Alacaoglu, Ahmet (author)
- Ecole Polytech Fed Lausanne EPFL, Switzerland
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- Malitskyi, Yurii (author)
- Linköpings universitet,Tillämpad matematik,Tekniska fakulteten
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- Cevher, Volkan (author)
- Ecole Polytech Fed Lausanne EPFL, Switzerland
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(creator_code:org_t)
- 2021-08-19
- 2021
- English.
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In: Computational optimization and applications. - : Springer Nature. - 0926-6003 .- 1573-2894. ; 80:2, s. 321-346
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Abstract
Subject headings
Close
- We propose a variance reduced algorithm for solving monotone variational inequalities. Without assuming strong monotonicity, cocoercivity, or boundedness of the domain, we prove almost sure convergence of the iterates generated by the algorithm to a solution. In the monotone case, the ergodic average converges with the optimal O(1/k) rate of convergence. When strong monotonicity is assumed, the algorithm converges linearly, without requiring the knowledge of strong monotonicity constant. We finalize with extensions and applications of our results to monotone inclusions, a class of non-monotone variational inequalities and Bregman projections.
Subject headings
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Keyword
- Variational inequalities; Stochastic variance reduction; Finite-sum structure; Saddle point problems; Monotone inclusions
Publication and Content Type
- ref (subject category)
- art (subject category)
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