Global convergence of a memory gradient method with closed-form step size formula

Nora Merabet

doi:10.3934/proc.2007.2007.721

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2007, Volume 2007: 721-730. Doi: 10.3934/proc.2007.2007.721 open access

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Global convergence of a memory gradient method with closed-form step size formula

Nora Merabet^1,

1.
UAE University, Department of Matematical Sciences, P.O. Box 17551, Al-Ain, United Arab Emirates

Received: August 31, 2006

Revised: May 31, 2007

Published: August 2007

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Abstract

The memory gradient method is used to solve large scale unconstrained optimization problems. We investigate a closed-form step size formula given by a finite number of iterates ofWeiszfeld’s algorithm to compute the step size for a memory gradient method. This formula can be classified as a no-line search procedure since no stopping criteria is involved to ensure convergence, unlike the classical line search procedures. We show the global convergence of the memory gradient method, under weaker conditions.

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Mathematics Subject Classification: Primary: 90C30, 65K05; Secondary: 49M37.

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