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

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Listed:
  • María de los Ángeles Martínez

    (Universidad Nacional de Córdoba)

  • Damián Fernández

    (Universidad Nacional de Córdoba)

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.

Suggested Citation

  • María de los Ángeles Martínez & Damián Fernández, 2019. "On the Local and Superlinear Convergence of a Secant Modified Linear-Programming-Newton Method," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 993-1010, March.
    • Handle: RePEc:spr:joptap:v:180:y:2019:i:3:d:10.1007_s10957-018-1407-1
    DOI: 10.1007/s10957-018-1407-1
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    References listed on IDEAS

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    1. Andreas Fischer & Markus Herrich & Alexey Izmailov & Mikhail Solodov, 2016. "Convergence conditions for Newton-type methods applied to complementarity systems with nonisolated solutions," Computational Optimization and Applications, Springer, vol. 63(2), pages 425-459, March.
    2. Alexey Izmailov & Mikhail Solodov, 2014. "On error bounds and Newton-type methods for generalized Nash equilibrium problems," Computational Optimization and Applications, Springer, vol. 59(1), pages 201-218, October.
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