The modified quasi-Newton methods for solving unconstrained optimization problems

Abstract

The usual quasi-Newton method at each iteration utilize the gradients and ignores the available function value information. In this paper, we employ Taylor formula and introduce a new quasi-Newton method, which uses both available gradient and function value information. This method approximates the Hessian matrix with excellent accuracy. The global convergence of these method associated to a general line search rule will be also shown. In addition, we will show that average performance of proposed algorithm is better than some proposed methods.