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On some steplength approaches for proximal algorithms

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  • Porta, Federica
  • Loris, Ignace

Abstract

We discuss a number of novel steplength selection schemes for proximal-based convex optimization algorithms. In particular, we consider the problem where the Lipschitz constant of the gradient of the smooth part of the objective function is unknown. We generalize two optimization algorithms of Khobotov type and prove convergence. We also take into account possible inaccurate computation of the proximal operator of the non-smooth part of the objective function. Secondly, we show convergence of an iterative algorithm with Armijo-type steplength rule, and discuss its use with an approximate computation of the proximal operator. Numerical experiments show the efficiency of the methods in comparison to some existing schemes.

Suggested Citation

  • Porta, Federica & Loris, Ignace, 2015. "On some steplength approaches for proximal algorithms," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 345-362.
    • Handle: RePEc:eee:apmaco:v:253:y:2015:i:c:p:345-362
    DOI: 10.1016/j.amc.2014.12.079
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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.
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    Cited by:

    1. Bonettini, S. & Prato, M. & Rebegoldi, S., 2021. "New convergence results for the inexact variable metric forward–backward method," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    2. Bubba, Tatiana A. & Porta, Federica & Zanghirati, Gaetano & Bonettini, Silvia, 2018. "A nonsmooth regularization approach based on shearlets for Poisson noise removal in ROI tomography," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 131-152.

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