Journal of Applied and Numerical Optimization

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DOI: 10.23952/jano.6.2024.1.05
Volume 6, Issue 1, 1 April 2024, Pages 83-96

 

Abstract. The split feasibility problem (SFP), which provides a unified framework to model a wide range of inverse problems, has received much considerable attention in the literature. However, how to efficiently solve SFPs is still an interesting topic. In this paper, we introduce a block-wise formulation for algorithmic design. Specifically, we first introduce an auxiliary variable to formulate the original SFP as a constrained minimization problem with a block structure, which paves a new way to find solutions of SFPs. Then, we show that the employments of some classical gradient-type optimization algorithms produce very simple, yet quite efficient iterative schemes to find a solution of SFPs when the underlying block structure could be exploited. The parallel iterative schemes of the proposed block-wise algorithms are not only efficient to deal with the case that the projections onto the convex sets have explicit representations, but also are possibly valuable for solving large-scale SFPs without explicit projections onto the underlying sets. Some numerical results on synthetic examples support the idea of this paper.

 

How to Cite this Article:
Z. Wang, H. He, Solving split feasibility problems via block-wise formulation, J. Appl. Numer. Optim. 6 (2024), 83-96.