Convergence of prox-regularization methods for generalized fractional programming

Ahmed Roubi

RAIRO - Operations Research - Recherche Opérationnelle (2002)

  • Volume: 36, Issue: 1, page 73-94
  • ISSN: 0399-0559

Abstract

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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 η k -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].

How to cite

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Roubi, Ahmed. "Convergence of prox-regularization methods for generalized fractional programming." RAIRO - Operations Research - Recherche Opérationnelle 36.1 (2002): 73-94. <http://eudml.org/doc/245897>.

@article{Roubi2002,
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 $\eta _k$-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].},
author = {Roubi, Ahmed},
journal = {RAIRO - Operations Research - Recherche Opérationnelle},
keywords = {generalized fractional programs; Dinkelbach-type algorithms; proximal point algorithm; rate of convergence; Generalized fractional programs, Dinkelbach-type algorithms, proximal point algorithm, rate of convergence.},
language = {eng},
number = {1},
pages = {73-94},
publisher = {EDP-Sciences},
title = {Convergence of prox-regularization methods for generalized fractional programming},
url = {http://eudml.org/doc/245897},
volume = {36},
year = {2002},
}

TY - JOUR
AU - Roubi, Ahmed
TI - Convergence of prox-regularization methods for generalized fractional programming
JO - RAIRO - Operations Research - Recherche Opérationnelle
PY - 2002
PB - EDP-Sciences
VL - 36
IS - 1
SP - 73
EP - 94
AB - 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 $\eta _k$-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].
LA - eng
KW - generalized fractional programs; Dinkelbach-type algorithms; proximal point algorithm; rate of convergence; Generalized fractional programs, Dinkelbach-type algorithms, proximal point algorithm, rate of convergence.
UR - http://eudml.org/doc/245897
ER -

References

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  11. [11] I. Ekeland and R. Temam, Analyse Convexe et Problèmes Variationnels. Gauthier-Villars, Paris, Bruxelles, Montréal (1974). Zbl0281.49001MR463993
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