A subgradient method with constant step-size for ℓ1 -composite optimization

A. Scagliotti, P. Colli Franzone

Publikation: Beitrag in FachzeitschriftArtikelBegutachtung

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 ℓ1-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.

OriginalspracheEnglisch
Seiten (von - bis)471-490
Seitenumfang20
FachzeitschriftBolletino dell Unione Matematica Italiana
Jahrgang17
Ausgabenummer2
DOIs
PublikationsstatusVeröffentlicht - Juni 2024

Fingerprint

Untersuchen Sie die Forschungsthemen von „A subgradient method with constant step-size for ℓ1 -composite optimization“. Zusammen bilden sie einen einzigartigen Fingerprint.

Dieses zitieren