Proximal Gradient Algorithms Under Local Lipschitz Gradient Continuity View Full Text


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Article Info

DATE

2022-07-06

AUTHORS

Alberto De Marchi, Andreas Themelis

ABSTRACT

Composite optimization offers a powerful modeling tool for a variety of applications and is often numerically solved by means of proximal gradient methods. In this paper, we consider fully nonconvex composite problems under only local Lipschitz gradient continuity for the smooth part of the objective function. We investigate an adaptive scheme for PANOC-type methods (Stella et al. in Proceedings of the IEEE 56th CDC, 2017), namely accelerated linesearch algorithms requiring only the simple oracle of proximal gradient. While including the classical proximal gradient method, our theoretical results cover a broader class of algorithms and provide convergence guarantees for accelerated methods with possibly inexact computation of the proximal mapping. These findings have also significant practical impact, as they widen scope and performance of existing, and possibly future, general purpose optimization software that invoke PANOC as inner solver. More... »

PAGES

771-794

References to SciGraph publications

  • 2017-02-14. Further properties of the forward–backward envelope with applications to difference-of-convex programming in COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
  • 1998. Variational Analysis in NONE
  • 2011-05-09. Proximal Splitting Methods in Signal Processing in FIXED-POINT ALGORITHMS FOR INVERSE PROBLEMS IN SCIENCE AND ENGINEERING
  • 2019-11-07. On the Acceleration of Forward-Backward Splitting via an Inexact Newton Method in SPLITTING ALGORITHMS, MODERN OPERATOR THEORY, AND APPLICATIONS
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    http://scigraph.springernature.com/pub.10.1007/s10957-022-02048-5

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    http://dx.doi.org/10.1007/s10957-022-02048-5

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    https://app.dimensions.ai/details/publication/pub.1149271708


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