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Step lengths in BFGS method for monotone gradients

Yunda Dong(ydong***at***zzu.edu.cn)

Abstract: In this paper, we consider how to directly apply the BFGS method to finding a zero point of any given monotone gradient and thus suggest new conditions to locate the corresponding step lengths. The suggested conditions involve curvature condition and merely use gradients' computations. Furthermore, they can guarantee convergence without any other restrictions. Finally, preliminary numerical experiments indicate their practical effectiveness in solving some systems of nonlinear equations arising in boundary value problems and others.

Keywords: Monotone gradient ; Quasi-Newton method; BFGS method; Convergence

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Nonlinear Optimization (Unconstrained Optimization )

Citation:

Download: [PDF]

Entry Submitted: 07/26/2016
Entry Accepted: 07/26/2016
Entry Last Modified: 07/26/2016

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