Abstract

In this study, a new self-scaling variable metric (VM)-updating method for solving nonlinear unconstrained optimization problems is presented. The general strategy of (New VM-updating) is to propose a new quasi-newton condition used for update the usual DFP Hessian to a number of times in a way to be specified in some iteration with PCG method to improve the performance of the Hessian approximation. We show that it produces a positive definite matrix. Experimental results indicate that the new suggested method was more efficient than the standard DFP method, with respect to the number of functions evaluations (NOF) and number of iterations (NOI).