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The Newton Method

In: Modern Numerical Nonlinear Optimization

Author

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  • Neculai Andrei

    (Center for Advanced Modeling and Optimization)

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.

Suggested Citation

  • Neculai Andrei, 2022. "The Newton Method," Springer Optimization and Its Applications, in: Modern Numerical Nonlinear Optimization, chapter 4, pages 109-168, Springer.
    • Handle: RePEc:spr:spochp:978-3-031-08720-2_4
    DOI: 10.1007/978-3-031-08720-2_4
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