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We propose to use the proximal point algorithm to regularize a “dual” problem of generalized fractional programs (GFP). The proposed technique leads to a new dual algorithm that generates a sequence which converges from below to the minimal value of the considered problem. At each step, the proposed algorithm solves approximately an auxiliary problem with a unique dual solution whose every cluster point gives a solution to the dual problem. In the exact minimization case, the sequence of dual solutions converges to an optimal dual solution. For a class of functions, including the linear case, the convergence of the dual values is at least linear.
Accepté le :
DOI : 10.1051/ro/2017004
Keywords: Multi-ratio fractional programs, Dinkelbach-type algorithms, Lagrange duality, proximal point algorithm
El Haffari, Mostafa 1 ; Roubi, Ahmed 1
@article{RO_2017__51_4_985_0,
author = {El Haffari, Mostafa and Roubi, Ahmed},
title = {Convergence of a proximal algorithm for solving the dual of a generalized fractional program},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {985--1004},
publisher = {EDP-Sciences},
volume = {51},
number = {4},
year = {2017},
doi = {10.1051/ro/2017004},
mrnumber = {3783931},
zbl = {1393.90113},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ro/2017004/}
}
TY - JOUR AU - El Haffari, Mostafa AU - Roubi, Ahmed TI - Convergence of a proximal algorithm for solving the dual of a generalized fractional program JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2017 SP - 985 EP - 1004 VL - 51 IS - 4 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ro/2017004/ DO - 10.1051/ro/2017004 LA - en ID - RO_2017__51_4_985_0 ER -
%0 Journal Article %A El Haffari, Mostafa %A Roubi, Ahmed %T Convergence of a proximal algorithm for solving the dual of a generalized fractional program %J RAIRO - Operations Research - Recherche Opérationnelle %D 2017 %P 985-1004 %V 51 %N 4 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ro/2017004/ %R 10.1051/ro/2017004 %G en %F RO_2017__51_4_985_0
El Haffari, Mostafa; Roubi, Ahmed. Convergence of a proximal algorithm for solving the dual of a generalized fractional program. RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 4, pp. 985-1004. doi: 10.1051/ro/2017004
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