Convergence properties of monotone and nonmonotone proximal gradient methods revisited
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- Composite optimization problems, where the sum of a smooth and a merely lower semicontinuous function has to be minimized, are often tackled numerically by means of proximal gradient methods as soon as the lower semicontinuous part of the objective function is of simple enough structure. The available convergence theory associated with these methods (mostly) requires the derivative of the smooth part of the objective function to be (globally) Lipschitz continuous, and this might be a restrictive assumption in some practically relevantComposite optimization problems, where the sum of a smooth and a merely lower semicontinuous function has to be minimized, are often tackled numerically by means of proximal gradient methods as soon as the lower semicontinuous part of the objective function is of simple enough structure. The available convergence theory associated with these methods (mostly) requires the derivative of the smooth part of the objective function to be (globally) Lipschitz continuous, and this might be a restrictive assumption in some practically relevant scenarios. In this paper, we readdress this classical topic and provide convergence results for the classical (monotone) proximal gradient method and one of its nonmonotone extensions which are applicable in the absence of (strong) Lipschitz assumptions. This is possible since, for the price of forgoing convergence rates, we omit the use of descent-type lemmas in our analysis.…
Autor(en): | Christian KanzowORCiD, Patrick Mehlitz |
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URN: | urn:nbn:de:bvb:20-opus-324351 |
Dokumentart: | Artikel / Aufsatz in einer Zeitschrift |
Institute der Universität: | Fakultät für Mathematik und Informatik / Institut für Mathematik |
Sprache der Veröffentlichung: | Englisch |
Titel des übergeordneten Werkes / der Zeitschrift (Englisch): | Journal of Optimization Theory and Applications |
ISSN: | 0022-3239 |
Erscheinungsjahr: | 2022 |
Band / Jahrgang: | 195 |
Heft / Ausgabe: | 2 |
Seitenangabe: | 624-646 |
Originalveröffentlichung / Quelle: | Journal of Optimization Theory and Applications (2023) 195:2, 624-646 DOI: 10.1007/s10957-022-02101-3 |
DOI: | https://doi.org/10.1007/s10957-022-02101-3 |
Allgemeine fachliche Zuordnung (DDC-Klassifikation): | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Freie Schlagwort(e): | non-Lipschitz optimization; nonsmooth optimization; proximal gradient method |
Fachklassifikation Mathematik (MSC): | 49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Jxx Existence theories / 49J52 Nonsmooth analysis [See also 46G05, 58C50, 90C56] |
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C30 Nonlinear programming | |
Datum der Freischaltung: | 27.02.2024 |
Lizenz (Deutsch): | ![]() |