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

V. Kanwar | Zendy; Kapil K. Sharma | Zendy; Ramandeep Behl | Zendy

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

Author(s) -

V. Kanwar,

Kapil K. Sharma,

Ramandeep Behl

Publication year - 2010

Publication title -

intelligent information management

Language(s) - English

Resource type - Journals

eISSN - 2160-5920

pISSN - 2160-5912

DOI - 10.4236/iim.2010.21005

Subject(s) - newton's method , convergence (economics) , nonlinear system , mathematics , logarithm , local convergence , steffensen's method , mathematical optimization , nonlinear programming , quadrature (astronomy) , newton's method in optimization , computer science , mathematical analysis , iterative method , physics , engineering , quantum mechanics , electrical engineering , economics , economic growth

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

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