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Superiorization with a Projected Subgradient Algorithm on the Solution Sets of Common Fixed Point Problems

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  • Alexander J. Zaslavski

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

Abstract

In this work, we investigate a minimization problem with a convex objective function on a domain, which is the solution set of a common fixed point problem with a finite family of nonexpansive mappings. Our algorithm is a combination of a projected subgradient algorithm and string-averaging projection method with variable strings and variable weights. This algorithm generates a sequence of iterates which are approximate solutions of the corresponding fixed point problem. Additionally, either this sequence also has a minimizing subsequence for our optimization problem or the sequence is strictly Fejer monotone regarding the approximate solution set of the common fixed point problem.

Suggested Citation

  • Alexander J. Zaslavski, 2023. "Superiorization with a Projected Subgradient Algorithm on the Solution Sets of Common Fixed Point Problems," Mathematics, MDPI, vol. 11(21), pages 1-12, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:21:p:4536-:d:1273761
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    References listed on IDEAS

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    1. Yair Censor & Alexander J. Zaslavski, 2015. "Strict Fejér Monotonicity by Superiorization of Feasibility-Seeking Projection Methods," Journal of Optimization Theory and Applications, Springer, vol. 165(1), pages 172-187, April.
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