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  1. Home > Articles & Issues >
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  3. Proximal gradient me ...
Article

Proximal gradient methods beyond monotony

Alberto De Marchi (1)
(1) Universität der Bundeswehr München
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Open on arXiv
Submitted on
November 10, 2022
Accepted on
May 25, 2023
Published on
June 2, 2023
Last modified on
June 2, 2023
Volume 4
Volume 4
Original research articles
DOI
10.46298/jnsao-2023-10290
License
Attribution 4.0 International (CC BY 4.0)
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Proximal gradient methods beyond monotony

Alberto De Marchi (1)
(1) Universität der Bundeswehr München
Abstract
We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal gradient methods, which often rely on a line search procedure as globalization mechanism. We consider an adaptive nonmonotone proximal gradient scheme based on an averaged merit function and establish asymptotic convergence guarantees under weak assumptions, delivering results on par with the monotone strategy. Global worst-case rates for the iterates and a stationarity measure are also derived. Finally, a numerical example indicates the potential of nonmonotonicity and spectral approximations. Comment: 18 pages, 1 algorithm, 1 figure
Keywords
  • Mathematics - Optimization and Control
Mathematics Subject Classification 2020
  • 49J52 - Nonsmooth analysis
  • 65K05 - Numerical mathematical programming methods
  • 90C26 - Nonconvex programming, global optimization
  • 90C52 - Methods of reduced gradient type
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