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

Alexander J. Zaslavski ()
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Alexander J. Zaslavski: Department of Mathematics, The Technion—Israel Institute of Technology, 32000 Haifa, Israel

Mathematics, 2023, vol. 11, issue 21, 1-12

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.

Keywords: constrained minimization; common fixed point problem; dynamic string-averaging projections; subgradients (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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