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.