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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; roubi@uh1.ac.ma.
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Abstract

We analyze the convergence of the prox-regularization algorithms introduced in [1], to solve generalized fractional programs, without assuming that the optimal solutions set of the considered problem is nonempty, and since the objective functions are variable with respect to the iterations in the auxiliary problems generated by Dinkelbach-type algorithms DT1 and DT2, we consider that the regularizing parameter is also variable. On the other hand we study the convergence when the iterates are only ηk-minimizers of the auxiliary problems. This situation is more general than the one considered in [1]. We also give some results concerning the rate of convergence of these algorithms, and show that it is linear and some times superlinear for some classes of functions. Illustrations by numerical examples are given 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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