A family of quasi-Newton methods for unconstrained optimization problems. (3rd October 2018)

• Record Type: Journal Article
• Authors: Salim, M. S.; Ahmed, A. I.
• Is Part Of: Optimization. Volume 67:Number 10(2018)
• Page Start: 1717
• Page End: 1727
• Publication Date: 2018-10-03
• Subjects: Unconstrained optimization -- quasi-Newton methods -- quadratic convergence -- descent methods; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1487423
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: 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.