Global Convergence Property of Scaled Two-Step BFGS Method

Abstract

This paper is aimed to extend the scheme of self scaling, appropriate for the quasi-Newton methods, to the two-step quasi-Newton methods. The scaling scheme has been performed during the main approach of updating the current Hessian approximation and prior to the computation of the next quasi-Newton direction whenever necessary. Global convergence property of the new method is explored on uniformly convex functions with the standard Wolfe line search. Preliminary numerical testing has been performed showing that this technique improves the performance of the two-step method substantially.