On the behavior of the gradient norm in the steepest descent method

Jorge Nocedal; Annick Sartenaer; Ciyou Zhu

On the behavior of the gradient norm in the steepest descent method

Jorge Nocedal, Annick Sartenaer, Ciyou Zhu

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Résumé

Il est connu que la norme du gradient peut ne pas se comporter de manière fiable comme critère d'arret en optimisation sans contraintes, et qu'elle présente souvent un comportement oscillatoire durant le processus d'optimisation. Dand ce projet, nous avons étudie les propriétés de la norme du gradient pour la méthode de la plus forte pente appliquée a des fonctions quadratiques. Nous avons aussi développé quelques observation générales applicables aux problèmes non-linéaires, mettant en corrélation la norme du gradient, la valeur de la fonction objective, et le chemin engendré par les itérés.

langue originale	Anglais
Pages (de - à)	5-35
Nombre de pages	31
journal	Computational Optimization and Application
Volume	22
Numéro de publication	1
Etat de la publication	Publié - 2002

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title = "On the behavior of the gradient norm in the steepest descent method",

abstract = "It is well known that the norm of the gradient may be unreliable as a stopping test in unconstrained optimization, and that it often exhibits oscillations in the course of the optimization. In this paper we present results describing the properties of the gradient norm for the steepest descent method applied to quadratic objective functions. We also make some general observations that apply to nonlinear problems, relating the gradient norm, the objective function value, and the path generated by the iterates. ",

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AU - Nocedal, Jorge

AU - Sartenaer, Annick

AU - Zhu, Ciyou

PY - 2002

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N2 - It is well known that the norm of the gradient may be unreliable as a stopping test in unconstrained optimization, and that it often exhibits oscillations in the course of the optimization. In this paper we present results describing the properties of the gradient norm for the steepest descent method applied to quadratic objective functions. We also make some general observations that apply to nonlinear problems, relating the gradient norm, the objective function value, and the path generated by the iterates.

AB - It is well known that the norm of the gradient may be unreliable as a stopping test in unconstrained optimization, and that it often exhibits oscillations in the course of the optimization. In this paper we present results describing the properties of the gradient norm for the steepest descent method applied to quadratic objective functions. We also make some general observations that apply to nonlinear problems, relating the gradient norm, the objective function value, and the path generated by the iterates.

KW - nonlinear optimization

KW - unconstrained optimization

KW - behavior of the gradeint norm

KW - steepest descent method

M3 - Article

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SP - 5

EP - 35

JO - Computational Optimization and Application

JF - Computational Optimization and Application

IS - 1

ER -

On the behavior of the gradient norm in the steepest descent method

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