New Variants of Newton’s Method for Nonlinear Unconstrained Optimization Problems

V. KANWAR, Kapil K. SHARMA, Ramandeep BEHL

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DOI: 10.4236/iim.2010.21005                

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.

Keywords

unconstrained optimization, Newton’s method, order of convergence, power means, initial guess

Conflicts of Interest

The authors declare no conflicts of interest.

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