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

Pages: 721 - 730, Issue Special, September 2007

 Abstract        Full Text (191.7K)              

Nora Merabet - UAE University, Department of Matematical Sciences, P.O. Box 17551, Al-Ain, United Arab Emirates, United Arab Emirates (email)

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.

Keywords:  Memory gradient method, closed-form step-size formula, global convergence.
Mathematics Subject Classification:  Primary: 90C30, 65K05; Secondary: 49M37.

Received: September 2006;      Revised: June 2007;      Published: September 2007.