Yaxuan Zhang, Liqian Qin, Two self-adaptive CQ algorithms for the split feasibility problem with multiple output sets, Vol. 2024 (2024), Article ID 5, pp. 1-19

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DOI: 10.23952/jnfa.2024.5

Received December 15, 2023; Accepted February 4, 2024; Published March 5, 2024

Abstract. The split feasibility problem with multiple output sets is to find a point $x^{*}\in \bigcap_{i=1}^{t}C_{i}$ such that $A_jx^*\in Q_j,$ $j=1,2,\ldots,r$ where $C_{i}\subset H$ and $Q_{j}\subset {H}_{j}$ are nonempty, convex, and closed subsets, $H$ and $H_j$ are Hilbert spaces, and $A_j: {H}\to {H}_j$ are linear and bounded operators. In this paper, we present two self-adaptive ball-relaxed CQ algorithms. Under mild conditions, we establish strong convergence and provide numerical experiments to illustrate the effectiveness of the proposed algorithms.

How to Cite this Article:
Y. Zhang, L. Qin, Two self-adaptive CQ algorithms for the split feasibility problem with multiple output sets, J. Nonlinear Funct. Anal. 2024 (2024) 5.