Prox-dual regularization algorithm for generalized fractional programs
Mostafa El Haffari, ,Laboratoire MISI, Faculté des Sciences et Techniques, Univ. Hassan 1,26000 Settat, Morocco, Ahmed Roubi · Journal of Industrial and Management Optimization · 2017
Prox-regularization algorithms for solving generalized fractional programs (GFP) were already considered by several authors. Since the standard 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 fractional 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 fractional 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.