JOURNAL OF INDUSTRIAL AND doi:10.3934/jimo.2017028 MANAGEMENT OPTIMIZATION Volume 13, Number 4, October 2017 pp. 1991–2013 PROX-DUAL REGULARIZATION ALGORITHM FOR GENERALIZED FRACTIONAL PROGRAMS Mostafa El Haffari Laboratoire MISI, Facult´ e des Sciences et Techniques Univ. Hassan 1 26000 Settat, Morocco Ahmed Roubi ∗ Laboratoire MISI, Facult´ e des Sciences et Techniques Univ. Hassan 1 26000 Settat, Morocco (Communicated by Vladimir Shikhman) Abstract. Prox-regularization algorithms for solving generalized fractional programs (GFP) were already considered by several authors. Since the stan- dard dual of a generalized fractional program has not generally the form of GFP, these approaches can not apply directly to the dual problem. In this paper, we propose a primal-dual algorithm for solving convex generalized frac- tional programs. That is, we use a prox-regularization method to the dual problem that generates a sequence of auxiliary dual problems with unique solutions. So we can avoid the numerical difficulties that can occur if the frac- tional program does not have a unique solution. Our algorithm is based on Dinkelbach-type algorithms for generalized fractional programming, but uses a regularized parametric auxiliary problem. We establish then the convergence and rate of convergence of this new algorithm. 1. Introduction. In this paper, we will be interested to generalized fractional programs of the form (P ) λ ∗ = inf x∈X max i∈I  f i (x) g i (x)  where I = {1,...,m}, m ≥ 1, and X a non empty subset of R n . The functions f i and g i are defined on an open subset K containing X, continuous and satisfy g i (x) > 0 for all x ∈ X and i ∈ I . Problems of such type arise in management applications of goal programming, in mathematical economics and numerical analysis, and in telecommunications, in- formation theory and computer science. Applications of single and multi-ratio pro- gramming can be found in ([20], [16], [12]). 2010 Mathematics Subject Classification. Primary: 90C32, 49N15, 49M29, 49M37; Secondary: 49K35. Key words and phrases. Multi-ratio fractional programs, Dinkelbach-type algorithms, La- grangian duality, proximal point algorithm. The authors would like to thank the referees for their valuable comments. * Corresponding author: Ahmed Roubi. 1991