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New Variants of Newton’s Method for Nonlinear Unconstrained Optimization Problems
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Intelligent Information Management·Volume 02 (2010)·Pages 40–45·Published 27 January 2010·DOI10.4236/iim.2010.21005
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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.
Keywordsunconstrained optimizationNewton’s methodorder of convergencepower meansinitial guess
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