Notes on Newton’s Method After 1960

José Mario Martínez ()
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José Mario Martínez: University of Campinas, Institute of Mathematics, Statistics and Scientific Computing

A chapter in Advances in Mathematics and Applications, 2018, pp 203-218 from Springer

Abstract: Abstract Some Newtonian ideas will be reported with respect to research areas that emerged in numerical Mathematics after, approximately, 1960. For the problems of solving nonlinear equations and unconstrained optimization, Quasi-Newton methods, which stayed in the mainstream of numerical optimization for more than 30 years, will be motivated and discussed. The topic of complexity in unconstrained optimization will be introduced and some fundamental results will be rigorously proved. Newtonian algorithmic schemes in Linear Programming, which emerged after 1984 and presently represent competitive alternatives for large-scale problems, will be commented. Finally, surprising negative results concerning the capacity of Newton’s method to detect approximate solutions of constrained optimization problems will be reported.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-94015-1_9

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DOI: 10.1007/978-3-319-94015-1_9

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