TITLE:
New Variants of Newton’s Method for Nonlinear Unconstrained Optimization Problems
AUTHORS:
V. KANWAR, Kapil K. SHARMA, Ramandeep BEHL
KEYWORDS:
unconstrained optimization, Newton’s method, order of convergence, power means, initial guess
JOURNAL NAME:
Intelligent Information Management,
Vol.2 No.1,
January
27,
2010
ABSTRACT: In this paper, we propose new variants of Newton’s method based on quadrature formula and power mean for solving nonlinear unconstrained optimization problems. It is proved that the order of convergence of the proposed family is three. Numerical comparisons are made to show the performance of the presented methods. Furthermore, numerical experiments demonstrate that the logarithmic mean Newton’s method outperform the classical Newton’s and other variants of Newton’s method. MSC: 65H05.