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A Subgradient Method With Constant Step-Size for L1-Composite Optimization

MCML Authors

Abstract

Subgradient methods are the natural extension to the non-smooth case of the classical gradient descent for regular convex optimization problems. However, in general, they are characterized by slow convergence rates, and they require decreasing step-sizes to converge. In this paper we propose a subgradient method with constant step-size for composite convex objectives with -regularization. If the smooth term is strongly convex, we can establish a linear convergence result for the function values. This fact relies on an accurate choice of the element of the subdifferential used for the update, and on proper actions adopted when non-differentiability regions are crossed. Then, we propose an accelerated version of the algorithm, based on conservative inertial dynamics and on an adaptive restart strategy, that is guaranteed to achieve a linear convergence rate in the strongly convex case. Finally, we test the performances of our algorithms on some strongly and non-strongly convex examples.

article

Bollettino dell'Unione Matematica Italiana

17. Jun. 2024.

Authors

A. Scagliotti • P. Colli Franzone

Links

DOI

Research Area

 A2 | Mathematical Foundations

BibTeXKey: SC24

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