A new pair conjugate algorithm with an adaptive optimal step size

In this paper, a new adapted optimal step-size is designed to improve the efficiency of pair conjugate method. At each linear search an acceptable step- size is estimated during quadratic interpolation and this estimate is used as an initial trial step-size. The technique needs only additional gradient evaluation at each search direction. Also we have improved Armijo line search technique to be used together with the new optimal stepsize. The numerical results are more efficient than the results of the same method using the classical scheme for the linear search technique.