Memoryless quasi-Newton methods based on spectral-scaling Broyden family for unconstrained optimization

Memoryless quasi-Newton methods are studied for solving large- scale unconstrained optimization problems. Recently, memoryless quasi-Newton methods based on several kinds of updating formulas were proposed. Since the methods closely related to the conjugate gradient method, the methods are promising. In this paper, we propose a memoryless quasi-Newton method based on the Broyden family with the spectral-scaling secant condition. We focus on the convex and preconvex classes of the Broyden family, and we show that the proposed method satisfies the sufficient descent condition and con- verges globally. Finally, some numerical experiments are given.