The Newton Method

Neculai Andrei ()
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Neculai Andrei: Center for Advanced Modeling and Optimization

Chapter 4 in Modern Numerical Nonlinear Optimization, 2022, pp 109-168 from Springer

Abstract: Abstract In the panoply of the optimization methods and in general, for solving problems that have an algebraic mathematical model, the Newton method has a central position. The idea of this method is to approximate the mathematical model through a local affine or a local quadratic model. This chapter is dedicated to presenting the Newton method for solving algebraic nonlinear systems on the one hand and to minimizing smooth enough functions on the other one. It is proved that, initialized near solution, the Newton method is quadratic convergent to a minimum point of the minimizing function. Some modifications of the Newton method and the composite Newton method are also presented.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-031-08720-2_4

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DOI: 10.1007/978-3-031-08720-2_4

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