In this paper, we are concerned with the q-Fletcher-Reeves (q-FR) method for solving unconstrained optimization problems. The direction generated by the proposed method is a q-descent direction of the objective function which is computed using q-gradient. The q-gradient is a generalization of the classical gradient based on the q- derivative. Moreover, the q-FR method reduces to the classical version of FR method when q approaches 1. We prove that the proposed algorithm is globally convergent with the Armijo-type line search condition even if the objective function is nonconvex. Further, the numerical results show that the proposed method are very promising and competitive.
