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Journal of Optimization Theory and Applications

, Volume 180, Issue 3, pp 993–1010 | Cite as

On the Local and Superlinear Convergence of a Secant Modified Linear-Programming-Newton Method

  • María de los Ángeles MartínezEmail author
  • Damián Fernández
Article
  • 117 Downloads

Abstract

We present a superlinearly convergent method to solve a constrained system of nonlinear equations. The proposed procedure is an adaptation of the linear-programming-Newton method replacing the first-order information with a secant update. Thus, under mild assumptions, the method is able to find possible nonisolated solutions without computing any derivative and achieving a local superlinear rate of convergence. In addition to the convergence analysis, some numerical examples are presented in order to show the fulfillment of the expected rate of convergence.

Keywords

Constrained nonlinear system of equations Nonisolated solutions Quasi-Newton method Local superlinear convergence 

Mathematics Subject Classification

90C30 65K05 

Notes

Acknowledgements

This work was partially supported by FONCyT Grant PICT 2014-2534 and CONICET Grant PIP 112-201101-00050.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.CIEM, FaMAF, CONICETUniversidad Nacional de CórdobaCórdobaArgentina

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