A Class of Diagonal Quasi-Newton Methods for Large-Scale Convex Minimization

作者：Leong Wah June^*

来源：Bulletin of the Malaysian Mathematical Sciences Society, 2016, 39(4): 1659-1672.

DOI：10.1007/s40840-015-0117-1

• Large-scale convex minimization
• Quasi-Newton methods
• Diagonal updating
• Scaling
• Globally and R-linearly convergent

We study the convergence properties of a class of low memory methods for solving large-scale unconstrained problems. This class of methods belongs to that of quasi-Newton family, except for which the approximation to Hessian, at each step, is updated by means of a diagonal matrix. Using appropriate scaling, we show that the methods can be implemented so as to be globally and -linearly convergent with standard inexact line searches. Preliminary numerical results suggest that the methods are good alternative to other low memory methods such as the CG and spectral gradient methods.

• 出版日期2016-10