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Forward-reflected-backward method with variance reduction

Author

Listed:
  • Ahmet Alacaoglu

    (École Polytechnique Fédérale de Lausanne (EPFL))

  • Yura Malitsky

    (Linköping University)

  • Volkan Cevher

    (École Polytechnique Fédérale de Lausanne (EPFL))

Abstract

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.

Suggested Citation

  • Ahmet Alacaoglu & Yura Malitsky & Volkan Cevher, 2021. "Forward-reflected-backward method with variance reduction," Computational Optimization and Applications, Springer, vol. 80(2), pages 321-346, November.
    • Handle: RePEc:spr:coopap:v:80:y:2021:i:2:d:10.1007_s10589-021-00305-3
    DOI: 10.1007/s10589-021-00305-3
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    References listed on IDEAS

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    1. Cong Dang & Guanghui Lan, 2015. "On the convergence properties of non-Euclidean extragradient methods for variational inequalities with generalized monotone operators," Computational Optimization and Applications, Springer, vol. 60(2), pages 277-310, March.
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