| Issue |
RAIRO-Oper. Res.
Volume 51, Number 4, October-December 2017
|
|
|---|---|---|
| Page(s) | 985 - 1004 | |
| DOI | https://doi.org/10.1051/ro/2017004 | |
| Published online | 21 November 2017 | |
Convergence of a proximal algorithm for solving the dual of a generalized fractional program∗
Faculté des Sciences et Techniques, Settat, Morocco.
roubia@hotmail.com
Received: 9 December 2015
Accepted: 22 December 2016
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.
Mathematics Subject Classification: 90C30 / 90C32 / 49K35 / 49M29 / 49M37
Key words: Multi-ratio fractional programs / Dinkelbach-type algorithms / Lagrange duality / proximal point algorithm
© EDP Sciences, ROADEF, SMAI 2017
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