Improved Hessian approximation with modified secant equations for symmetric rank-one method

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:235

Article

Modarres, Farzin¹  Malik, Abu Hassan¹  Leong, Wah June¹ 

[1] Univ Putra Malaysia, Dept Math, Fac Sci, Serdang 43400, Selangor, Malaysia

关键词: Unconstrained minimization;    Symmetric rank-one update;    Secant equation;    Hessian approximation;   

DOI  :  10.1016/j.cam.2010.10.042

来源: Elsevier

【 摘 要 】

Symmetric rank-one (SR1) is one of the competitive formulas among the quasi-Newton (QN) methods. In this paper, we propose some modified SR1 updates based on the modified secant equations, which use both gradient and function information. Furthermore, to avoid the loss of positive definiteness and zero denominators of the new SR1 updates, we apply a restart procedure to this update. Three new algorithms are given to improve the Hessian approximation with modified secant equations for the SR1 method. Numerical results show that the proposed algorithms are very encouraging and the advantage of the proposed algorithms over the standard SR1 and BFGS updates is clearly observed. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free