The CG-BFGS Method for Unconstrained Optimization Problems

被引：0

作者：

Bin Ibrahim, Mohd Asrul Hery ^{[1
]}

Mamat, Mustafa ^{[2
]}

June, Leong Wah ^{[3
]}

Sofi, Azfi Zaidi Mohammad ^{[4
]}

机构：

[1] IUKL, Fac Appl Sci & Fdn, Kajang, Malaysia

[2] Univ Malaysia Terengganu UMT, Fac Sci & Technol, Dept Math, Terengganu, Malaysia

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

[4] Kolej Univ Islam Antarabangsa Selangor KUIS, Fac Sci & Informat Technol, Kajang, Selangor, Malaysia

来源：

PROCEEDINGS OF THE 21ST NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES (SKSM21): GERMINATION OF MATHEMATICAL SCIENCES EDUCATION AND RESEARCH TOWARDS GLOBAL SUSTAINABILITY | 2014年 / 1605卷

关键词：

Conjugate Gradient method; BFGS method; Search Direction; CONJUGATE-GRADIENT ALGORITHMS; QUASI-NEWTON METHODS; CONVERGENCE CONDITIONS; ASCENT METHODS; MINIMIZATION; SOFTWARE;

D O I：

10.1063/1.4887583

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we present a new search direction known as the CG-BFGS method, which uses the search direction of the conjugate gradient method approach in the quasi-Newton methods. The new algorithm is compared with the quasi-Newton methods in terms of the number of iterations and CPU-time. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is used as an updating formula for the approximation of the Hessian for both methods. Our numerical analysis provides strong evidence that our CG-BFGS method is more efficient than the ordinary BFGS method. Besides, we also prove that the new algorithm is globally convergent.

引用

页码：167 / 172

页数：6

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