Problèmes fractionnaires : tour d'horizonsur les applications et méthodes de résolution

Anass Nagih; Gérard Plateau

doi:10.1051/ro:1999118

Abstract

Fractional programming consists in optimizing a ratio oftwo functions subject to some constraints. Different versions of thismodel, linear or nonlinear, have applications in various fields likecombinatorial optimization, stochastic programming, data bases, andeconomy. Three resolution methods are presented: direct solution,parametric approach and solution of an equivalent problem.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Stancu-Minasian, I. M. 2006. A sixth bibliography of fractional programming. Optimization, Vol. 55, Issue. 4, p. 405.

Billionnet, Alain and Djebali, Karima 2006. Solution of a fractional combinatorial optimization problem by mixed integer programming. RAIRO - Operations Research, Vol. 40, Issue. 2, p. 97.

Chergui, Mohamed El-Amine and Moulaï, Mustapha 2008. An Exact Method for a Discrete Multiobjective Linear Fractional Optimization. Journal of Applied Mathematics and Decision Sciences, Vol. 2008, Issue. , p. 1.

Mehrjerdi, Yahia Zare 2011. Solving fractional programming problem through fuzzy goal setting and approximation. Applied Soft Computing, Vol. 11, Issue. 2, p. 1735.

Alfandari, L. Sadki, J. Plateau, A. and Nagih, A. 2013. Hybrid column generation for large-size Covering Integer Programs: Application to transportation planning. Computers & Operations Research, Vol. 40, Issue. 8, p. 1938.

Hu, Jian-Bing Lu, Guo-Ping Zhang, Shi-Bing and Zhao, Ling-Dong 2015. Lyapunov stability theorem about fractional system without and with delay. Communications in Nonlinear Science and Numerical Simulation, Vol. 20, Issue. 3, p. 905.

Boufi, K. and Roubi, A. 2017. Dual method of centers for solving generalized fractional programs. Journal of Global Optimization, Vol. 69, Issue. 2, p. 387.

El Haffari, Mostafa and Roubi, Ahmed 2017. Prox-dual regularization algorithm for generalized fractional programs. Journal of Industrial & Management Optimization, Vol. 13, Issue. 4, p. 1991.

Addoune, S. El Haffari, M. and Roubi, A. 2017. A proximal point algorithm for generalized fractional programs. Optimization, Vol. 66, Issue. 9, p. 1495.

Addoune, Smail Boufi, Karima and Roubi, Ahmed 2018. Proximal Bundle Algorithms for Nonlinearly Constrained Convex Minimax Fractional Programs. Journal of Optimization Theory and Applications, Vol. 179, Issue. 1, p. 212.

Boualam, H. and Roubi, A. 2019. Proximal bundle methods based on approximate subgradients for solving Lagrangian duals of minimax fractional programs. Journal of Global Optimization, Vol. 74, Issue. 2, p. 255.

Boufi, Karima and Roubi, Ahmed 2019. Duality Results and Dual Bundle Methods Based on the Dual Method of Centers for Minimax Fractional Programs. SIAM Journal on Optimization, Vol. 29, Issue. 2, p. 1578.

Boufi, K. and Roubi, A. 2019. Prox-regularization of the dual method of centers for generalized fractional programs. Optimization Methods and Software, Vol. 34, Issue. 3, p. 515.

Bennani, Ahlem Benterki, Djamel and Grar, Hassina 2021. Adaptive projection methods for linear fractional programming. RAIRO - Operations Research, Vol. 55, Issue. , p. S2383.

Raut, Mathbar Singh Mei, Dongming Bhattarai, Sanjay Panth, Rajendra Kooi, Kyler Mei, Hao and Wang, Guojian 2023. Development of Low-Threshold Detectors for Low-Mass Dark Matter Searches with a p-Type Germanium Detector Operated at Cryogenic Temperature. Journal of Low Temperature Physics, Vol. 212, Issue. 3-4, p. 138.

Boualam, Hssaine and Roubi, Ahmed 2023. Augmented Lagrangian dual for nonconvex minimax fractional programs and proximal bundle algorithms for its resolution. Journal of Industrial and Management Optimization, Vol. 19, Issue. 5, p. 3610.

Ghazi, A. and Roubi, A. 2023. Optimality conditions and DC-Dinkelbach-type algorithm for vector fractional programming problems with ratios of difference of convex functions. Optimization, p. 1.

Boufi, Karima Fadil, Abdessamad and Roubi, Ahmed 2024. Successive upper approximation methods for generalized fractional programs. RAIRO - Operations Research, Vol. 58, Issue. 4, p. 3119.

Article contents

Problèmes fractionnaires : tour d'horizonsur les applications et méthodes de résolution

Abstract

Keywords

Access options

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

Problèmes fractionnaires : tour d'horizonsur les applications et méthodes de résolution

Abstract

Keywords

Access options

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests