Newton’s iterates can converge to non-stationary points

In this note we discuss the convergence of Newton’s method for minimization. We present examples in which the Newton iterates satisfy the Wolfe conditions and the Hessian is positive definite at each step and yet the iterates converge to a non-stationary point. These examples answer a question posed...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Mathematical programming 2008-04, Vol.112 (2), p.327-334
1. Verfasser: Mascarenhas, Walter F.
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:In this note we discuss the convergence of Newton’s method for minimization. We present examples in which the Newton iterates satisfy the Wolfe conditions and the Hessian is positive definite at each step and yet the iterates converge to a non-stationary point. These examples answer a question posed by Fletcher in his 1987 book Practical methods of optimization .
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-006-0019-y