Geodesic
Convergence of a proximal algorithm for solving the dual of a generalized fractional program
El Haffari, Mostafa1 ; Roubi, Ahmed1
1 Faculté des Sciences et Techniques, Settat, Morocco.
RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 4, pp. 985-1004

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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.

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Accepté le :
DOI : 10.1051/ro/2017004
Classification : 90C30, 90C32, 49K35, 49M29, 49M37
Keywords: Multi-ratio fractional programs, Dinkelbach-type algorithms, Lagrange duality, proximal point algorithm

El Haffari, Mostafa 1 ; Roubi, Ahmed 1

1 Faculté des Sciences et Techniques, Settat, Morocco. 
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     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},
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     language = {en},
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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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