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Global Convergence of Algorithms Based on Unions of Non-Expansive Maps

Author

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  • Alexander J. Zaslavski

    (Department of Mathematics, Technion–Israel Institute of Technology, Haifa 32000, Israel)

Abstract

In his recent research, M. K. Tam (2018) considered a framework for the analysis of iterative algorithms which can be described in terms of a structured set-valued operator. At each point in the ambient space, the value of the operator can be expressed as a finite union of values of single-valued para-contracting operators. He showed that the associated fixed point iteration is locally convergent around strong fixed points. In the present paper we generalize the result of Tam and show the global convergence of his algorithm for an arbitrary starting point. An analogous result is also proven for the Krasnosel’ski–Mann iterations.

Suggested Citation

  • Alexander J. Zaslavski, 2023. "Global Convergence of Algorithms Based on Unions of Non-Expansive Maps," Mathematics, MDPI, vol. 11(14), pages 1-11, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3213-:d:1199752
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    References listed on IDEAS

    as
    1. Minh N. Dao & Matthew K. Tam, 2019. "Union Averaged Operators with Applications to Proximal Algorithms for Min-Convex Functions," Journal of Optimization Theory and Applications, Springer, vol. 181(1), pages 61-94, April.
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