The conjugate gradient (CG) algorithm is one of the most popular algorithms for solving nonlinear unconstrained optimization problems. The Hestenes-Stiefel (HS) conjugate gradient formula is relatively one of the most efficient methods developed in this century. In addition, the (HS) coefficient has the conjugacy condition regardless of the line search method used. In this paper, we use the original HS CG formula with q-gradient to construct a q-HS method. The convergence and q-descent descent with the strong Wolfe and standard Wolfe line searches are established. Due to the advantage of q-gradient, the search process starts from global at the beginning and reaches to local. Numerical results illustrate the efficiency of algorithm
