Modifying Of Barzilai and Borwein Method for Solving Large-Scale Unconstrained Optimization Problems.

In this paper we present a technique for computing the minimum value of an objective function in the frame of gradient descent methods based on combination of Barzilai and Borwein approximation of Hessian matrix of objective function and Lipchetz constant in the gradient flow algorithm which is derived from a system of ordinary differential equations associated to unconstrained optimization problem. This algorithm suitable for large- scale unconstrained optimization problems, computational results for this algorithm is given and compared with BB method showing a considerable improvement.