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Equations and Unconstrained Optimization

  • Alexey F. Izmailov
  • Mikhail V. Solodov
Chapter
Part of the Springer Series in Operations Research and Financial Engineering book series (ORFE)

Abstract

In this chapter, we start our discussion of Newton-type methods, which are based on the fundamental principle of linear/quadratic approximation of the problem data (or of some part of the problem data). The underlying idea is extremely important, as it serves as a foundation for numerous computationally efficient algorithms for optimization and variational problems. We also discuss linesearch and trust-region globalizations of local algorithms, as well as the case of semismooth problems.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Alexey F. Izmailov
    • 1
  • Mikhail V. Solodov
    • 2
  1. 1.Moscow State UniversityMoscowRussia
  2. 2.Instituto de Matemática Pura e AplicadaRio de JaneiroBrazil

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