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Convergence of Prox-Regularization Methods for Generalized Fractional Programming

Published online by Cambridge University Press:  15 July 2002

Ahmed Roubi
Ahmed Roubi*
Affiliation:
Faculté des Sciences et Techniques, Département de Mathématiques et Informatique, Route de Casablanca, BP. 577, Settat, Morocco; [email protected].
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Abstract

We analyze the convergence of the prox-regularization algorithmsintroduced in [1], to solve generalized fractional programs,without assuming that the optimal solutions set of the consideredproblem is nonempty, and since the objective functions arevariable with respect to the iterations in the auxiliary problemsgenerated by Dinkelbach-type algorithms DT1 and DT2, we considerthat the regularizing parameter is also variable. On the otherhand we study the convergence when the iterates are onlyηk -minimizers of the auxiliary problems. This situation ismore general than the one considered in [1]. We also give someresults concerning the rate of convergence of these algorithms,and show that it is linear and some times superlinear for someclasses of functions. Illustrations by numerical examples aregiven in [1].

Keywords

Generalized fractional programsDinkelbach-type algorithmsproximal point algorithmrate of convergence.
Type
Research Article
Information
RAIRO - Operations Research , Volume 36 , Issue 1 , January 2002 , pp. 73 - 94
Copyright
© EDP Sciences, 2002

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