Variational Problems: Local Methods

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


In this chapter, we present local analysis of Newton-type algorithms for variational problems, starting with the fundamental Josephy–Newton method for generalized equations. This method is an important extension of classical Newtonian techniques to more general variational problems. For example, as a specific application, the Josephy–Newton method provides a convenient tool for analyzing the sequential quadratic programming algorithm for optimization. We also discuss semismooth Newton methods for complementarity problems, and active-set methods with identifications based on error bounds.


Variational Inequality Newton Method Complementarity Problem Sequential Quadratic Programming Linear Complementarity Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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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