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The Proximal Point Method with Remotest Set Control for Maximal Monotone Operators and Quasi-Nonexpansive Mappings

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  • Alexander J. Zaslavski

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

Abstract

In the present paper, we use the proximal point method with remotest set control for find an approximate common zero of a finite collection of maximal monotone maps in a real Hilbert space under the presence of computational errors. We prove that the inexact proximal point method generates an approximate solution if these errors are summable. Also, we show that if the computational errors are small enough, then the inexact proximal point method generates approximate solutions

Suggested Citation

  • Alexander J. Zaslavski, 2025. "The Proximal Point Method with Remotest Set Control for Maximal Monotone Operators and Quasi-Nonexpansive Mappings," Mathematics, MDPI, vol. 13(14), pages 1-12, July.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:14:p:2282-:d:1702621
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    References listed on IDEAS

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    1. A. N. Iusem, 1998. "On Some Properties of Generalized Proximal Point Methods for Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 96(2), pages 337-362, February.
    2. O. Chaldi & Z. Chbani & H. Riahi, 2000. "Equilibrium Problems with Generalized Monotone Bifunctions and Applications to Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 105(2), pages 299-323, May.
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