Split feasibility problem with multiple sets: applications to data classification and imaging

doi:10.1080/00036811.2026.2636918

Split feasibility problem with multiple sets: applications to data classification and imaging

2026-03-01

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DOI：10.1080/00036811.2026.2636918

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This paper introduces a novel iterative algorithm for addressing the generalized split feasibility and fixed point problem with multiple output sets in the setting of Hilbert spaces. The proposed approach integrates the viscosity approximation technique with inertial extrapolation to accelerate convergence, while the incorporation of Tikhonov regularization enhances the stability of the iteration process. We establish strong convergence results that guarantee the algorithm converges to an element of the solution set under mild assumptions. To evaluate its practical efficiency, comprehensive numerical experiments are carried out on two real world applications: data classification and image recovery problems. The results reveal that the proposed method consistently outperforms several state of the art algorithms, achieving higher classification accuracy, well-balanced precision-recall performance and superior reconstruction quality. These findings confirm both the robustness and effectiveness of the method, highlighting its significant potential for broader applications in optimization theory, machine learning, and image processing.

Keywords:

Viscosity approximation

strong convergence

split feasibility problem

fixed point problem

Split feasibility problem with multiple sets: applications to data classification and imaging

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