A new quasi-newton equation on the gradient methods for optimization minimization problem

Abstract

The quasi-Newton equation is the very foundation of an assortment of the quasi-Newton methods for optimization minimization problem. In this paper, we deriving a new quasi-Newton equation based on the second-order Taylor’s series expansion. The global convergence is established underneath suitable conditions and numerical results are reported to show that the given algorithm is more effective than those of the normal BFGS method.