A family of quasi-Newton methods for unconstrained optimization problems

被引：10

作者：

Salim, M. S. ^{[1
]}

Ahmed, A. I. ^{[1
]}

机构：

[1] Al Azhar Univ, Fac Sci, Dept Math, Assiut, Egypt

来源：

OPTIMIZATION | 2018年 / 67卷 / 10期

关键词：

Unconstrained optimization; quasi-Newton methods; quadratic convergence; descent methods; CONJUGATE-GRADIENT METHOD; BFGS METHOD; DESCENT; CONVERGENCE;

D O I：

10.1080/02331934.2018.1487423

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

In this paper, we present a class of approximating matrices as a function of a scalar parameter that includes the Davidon-Fletcher-Powell and Broyden-Fletcher-Goldfarb-Shanno methods as special cases. A powerful iterative descent method for finding a local minimum of a function of several variables is described. The new method maintains the positive definiteness of the approximating matrices. For a region in which the function depends quadratically on the variables, no more than n iterations are required, where n is the number of variables. A set of computational results that verifies the superiority of the new method are presented.

引用

页码：1717 / 1727

页数：11

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