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2024 | OriginalPaper | Buchkapitel

7. A Perturbed Mann-Type Algorithm for Zeros of Maximal Monotone Mappings

verfasst von : Oumar Abdel Kader Aghrabatt, Aminata D. Diene, Ngalla Djitte

Erschienen in: Mathematics of Computer Science, Cybersecurity and Artificial Intelligence

Verlag: Springer Nature Switzerland

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Abstract

Das Kapitel befasst sich mit der Erforschung maximaler monotoner Abbildungen, einem entscheidenden Konzept für nichtlineare Analyse und Optimierung. Es beginnt damit, monotone und stark monotone Operatoren in realen Hilbert- und Banach-Räumen zu definieren und ihre Bedeutung in verschiedenen mathematischen Kontexten hervorzuheben. Das Hauptaugenmerk liegt auf der Entwicklung eines neuen iterativen Algorithmus zur Annäherung von Nullen an begrenzte maximale monotone Mappings, der bisherige Methoden vereinfacht und erweitert. Der Algorithmus ist so konzipiert, dass er effizienter ist und in einem breiteren Spektrum von Banach-Räumen anwendbar. Zusätzlich wendet das Kapitel diese Ergebnisse auf differenzierbare konvexe Minimierungsprobleme an und demonstriert den praktischen Nutzen des vorgeschlagenen Algorithmus. Die Beweismethode und die spezifischen Bedingungen, unter denen der Algorithmus stark konvergiert, werden ebenfalls hervorgehoben, was das Kapitel zu einer wertvollen Ressource für Forscher und Praktiker auf diesem Gebiet macht.
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Metadaten
Titel
A Perturbed Mann-Type Algorithm for Zeros of Maximal Monotone Mappings
verfasst von
Oumar Abdel Kader Aghrabatt
Aminata D. Diene
Ngalla Djitte
Copyright-Jahr
2024
Buch
Mathematics of Computer Science, Cybersecurity and Artificial Intelligence

Print ISBN: 978-3-031-66221-8

Electronic ISBN: 978-3-031-66222-5

Copyright-Jahr: 2024

DOI
https://doi.org/10.1007/978-3-031-66222-5_7

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