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A General Iterative Procedure to Solve Generalized Equations with Differentiable Multifunction

Author

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  • Michaël Gaydu

    (Université Antilles)

  • Gilson N. Silva

    (Universidade Federal de Goiás)

Abstract

Taking advantage of recent developments in the theory of generalized differentiation of multifunctions, we present in a unified manner a general iterative procedure for solving generalized equations. This procedure is based on a certain type of approximation of functions called point-based approximation together with a linearization of the multifunctions. Our theorem encompasses the Newton method and extends in the same time, many methods of resolution of generalized equations that have been developed during the last two decades.

Suggested Citation

  • Michaël Gaydu & Gilson N. Silva, 2020. "A General Iterative Procedure to Solve Generalized Equations with Differentiable Multifunction," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 207-222, April.
    • Handle: RePEc:spr:joptap:v:185:y:2020:i:1:d:10.1007_s10957-020-01635-8
    DOI: 10.1007/s10957-020-01635-8
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    References listed on IDEAS

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    1. D. Azé & C. C. Chou, 1995. "On a Newton Type Iterative Method for Solving Inclusions," Mathematics of Operations Research, INFORMS, vol. 20(4), pages 790-800, November.
    2. F. Aragón Artacho & A. Belyakov & A. Dontchev & M. López, 2014. "Local convergence of quasi-Newton methods under metric regularity," Computational Optimization and Applications, Springer, vol. 58(1), pages 225-247, May.
    3. Michaël Gaydu & Michel Geoffroy & Yvesner Marcelin, 2016. "Prederivatives of convex set-valued maps and applications to set optimization problems," Journal of Global Optimization, Springer, vol. 64(1), pages 141-158, January.
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    Cited by:

    1. Jiaxi Wang & Wei Ouyang, 2022. "Newton’s Method for Solving Generalized Equations Without Lipschitz Condition," Journal of Optimization Theory and Applications, Springer, vol. 192(2), pages 510-532, February.

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