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Modified Fejér sequences and applications

Author

Listed:
  • Junhong Lin

    (Istituto Italiano di Tecnologia and Massachusetts Institute of Technology)

  • Lorenzo Rosasco

    (Istituto Italiano di Tecnologia and Massachusetts Institute of Technology
    Università degli Studi di Genova)

  • Silvia Villa

    (Politecnico di Milano)

  • Ding-Xuan Zhou

    (City University of Hong Kong)

Abstract

In this note, we propose and study the notion of modified Fejér sequences. Within a Hilbert space setting, this property has been used to prove ergodic convergence of proximal incremental subgradient methods. Here we show that indeed it provides a unifying framework to prove convergence rates for objective function values of several optimization algorithms. In particular, our results apply to forward–backward splitting algorithm, incremental subgradient proximal algorithm, and the Douglas–Rachford splitting method including and generalizing known results.

Suggested Citation

  • Junhong Lin & Lorenzo Rosasco & Silvia Villa & Ding-Xuan Zhou, 2018. "Modified Fejér sequences and applications," Computational Optimization and Applications, Springer, vol. 71(1), pages 95-113, September.
    • Handle: RePEc:spr:coopap:v:71:y:2018:i:1:d:10.1007_s10589-017-9962-1
    DOI: 10.1007/s10589-017-9962-1
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    References listed on IDEAS

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    1. Patrick L. Combettes & Jean-Christophe Pesquet, 2011. "Proximal Splitting Methods in Signal Processing," Springer Optimization and Its Applications, in: Heinz H. Bauschke & Regina S. Burachik & Patrick L. Combettes & Veit Elser & D. Russell Luke & Henry (ed.), Fixed-Point Algorithms for Inverse Problems in Science and Engineering, chapter 0, pages 185-212, Springer.
    2. Larsson, Torbjorn & Patriksson, Michael & Stromberg, Ann-Brith, 2003. "On the convergence of conditional [var epsilon]-subgradient methods for convex programs and convex-concave saddle-point problems," European Journal of Operational Research, Elsevier, vol. 151(3), pages 461-473, December.
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