A New Kind of Quasi-Newton Equation Based on the Quadratic Model for Unconstrained Optimization

Abstract

In this article, a modified BFGS method is introduced based on an innovative quasi-Newton type equation built on the quadratic model. An important property of the introduced method is that it utilizes the function values and the available gradient values. We prove the global convergence property under some proper assumptions. Numerical findings are presented to show the efficacy of the algorithms proposed for practical computations.