Pischke, Nicholas ; Kohlenbach, Ulrich (2022)
Quantitative analysis of a subgradient-type method for equilibrium problems.
In: Numerical Algorithms, 90 (1)
doi: 10.1007/s11075-021-01184-9
Artikel, Bibliographie
Dies ist die neueste Version dieses Eintrags.
Kurzbeschreibung (Abstract)
We use techniques originating from the subdiscipline of mathematical logic called ‘proof mining’ to provide rates of metastability and—under a metric regularity assumption—rates of convergence for a subgradient-type algorithm solving the equilibrium problem in convex optimization over fixed-point sets of firmly nonexpansive mappings. The algorithm is due to H. Iiduka and I. Yamada who in 2009 gave a noneffective proof of its convergence. This case study illustrates the applicability of the logic-based abstract quantitative analysis of general forms of Fejér monotonicity as given by the second author in previous papers.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2022 |
| Autor(en): | Pischke, Nicholas ; Kohlenbach, Ulrich |
| Art des Eintrags: | Bibliographie |
| Titel: | Quantitative analysis of a subgradient-type method for equilibrium problems |
| Sprache: | Englisch |
| Publikationsjahr: | Mai 2022 |
| Verlag: | Springer Science |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Numerical Algorithms |
| Jahrgang/Volume einer Zeitschrift: | 90 |
| (Heft-)Nummer: | 1 |
| DOI: | 10.1007/s11075-021-01184-9 |
| Zugehörige Links: | |
| Kurzbeschreibung (Abstract): | We use techniques originating from the subdiscipline of mathematical logic called ‘proof mining’ to provide rates of metastability and—under a metric regularity assumption—rates of convergence for a subgradient-type algorithm solving the equilibrium problem in convex optimization over fixed-point sets of firmly nonexpansive mappings. The algorithm is due to H. Iiduka and I. Yamada who in 2009 gave a noneffective proof of its convergence. This case study illustrates the applicability of the logic-based abstract quantitative analysis of general forms of Fejér monotonicity as given by the second author in previous papers. |
| Freie Schlagworte: | Equilibrium problems, Firmly nonexpansive mappings, Subgradient-type method, Proof mining |
| Zusätzliche Informationen: | Erstveröffentlichung; Mathematics Subject Classification (2010) 47H06, 47J25, 90C33, 03F10 |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
| Fachbereich(e)/-gebiet(e): | 04 Fachbereich Mathematik 04 Fachbereich Mathematik > Logik |
| Hinterlegungsdatum: | 30 Sep 2024 11:20 |
| Letzte Änderung: | 30 Sep 2024 11:20 |
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| Suche nach Titel in: | TUfind oder in Google |
Verfügbare Versionen dieses Eintrags
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Quantitative analysis of a subgradient-type method for equilibrium problems. (deposited 24 Sep 2024 11:36)
- Quantitative analysis of a subgradient-type method for equilibrium problems. (deposited 30 Sep 2024 11:20) [Gegenwärtig angezeigt]
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