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On the interplay between acceleration and identification for the proximal gradient algorithm

Author

Listed:
  • Gilles Bareilles

    (Univ. Grenoble Alpes)

  • Franck Iutzeler

    (Univ. Grenoble Alpes)

Abstract

In this paper, we study the interplay between acceleration and structure identification for the proximal gradient algorithm. While acceleration is generally beneficial in terms of functional decrease, we report and analyze several cases where its interplay with identification has negative effects on the algorithm behavior (iterates oscillation, loss of structure, etc.). Then, we present a generic method that tames acceleration when structure identification may be at stake; it benefits from a convergence rate that matches the one of the accelerated proximal gradient under some qualifying condition. We show empirically that the proposed method is much more stable in terms of subspace identification compared to the accelerated proximal gradient method while keeping a similar functional decrease.

Suggested Citation

  • Gilles Bareilles & Franck Iutzeler, 2020. "On the interplay between acceleration and identification for the proximal gradient algorithm," Computational Optimization and Applications, Springer, vol. 77(2), pages 351-378, November.
    • Handle: RePEc:spr:coopap:v:77:y:2020:i:2:d:10.1007_s10589-020-00218-7
    DOI: 10.1007/s10589-020-00218-7
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    References listed on IDEAS

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    1. Franck Iutzeler & Jérôme Malick, 2018. "On the Proximal Gradient Algorithm with Alternated Inertia," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 688-710, March.
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