Modified Secant-type methods for unconstrained optimization

Kahya E.

APPLIED MATHEMATICS AND COMPUTATION, vol.181, no.2, pp.1349-1356, 2006 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 181 Issue: 2
  • Publication Date: 2006
  • Doi Number: 10.1016/j.amc.2006.03.003
  • Journal Name: APPLIED MATHEMATICS AND COMPUTATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1349-1356
  • Keywords: unconstrained optimization, univariate optimization, Newton method, Secant method, test functions, initial point, UNIDIMENSIONAL SEARCH METHOD
  • Eskisehir Osmangazi University Affiliated: Yes

Abstract

For solving nonlinear, univariate and unconstrained optimization problems, Newton method is an important and basic method which convergences quadratically. In this paper, we suggest a family of three new modifications of the classical Secant method where the iteration formula including an approximation of f'(x(k)) is satisfied by a recursive scheme. The efficiencies of the new methods are analyzed in terms of the most popular and widely used criterion; the number of iterations, in comparison with the Newton and Secant methods using six test functions. (c) 2006 Elsevier Inc. All rights reserved.