Sur les performances des méthodes projectives pour les problèmes d'optimisation fractionnaires

Abstract

This thesis concerns the resolution of an optimization problem of linear fractional programming type. Initially, the considered problem will be transformed into an equivalent linear program via an adequate formulation while avoiding the increase of the dimension of the initial problem, then solved by means of a interior point projective methods. In a second step, using the variational inequalities problems, we solved the linear fractional program by a recent projection method. Finally, we have successfully established the numerical implementation of the resulting algorithms. The numerical results obtained are satisfactory, highlighting the effectiveness of the approach of interior point methods.