Journal of Applied and Numerical Optimization

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DOI: 10.23952/jano.2.2020.3.08
Volume 2, Issue 3, 31 December 2020, Pages 387-399

 

Abstract. The split feasibility problem (SFP) provides a powerful unified model to characterize many real-world inverse problems arising from image reconstruction and intensity-modulated radiation therapy. As we know, the original CQ algorithm, which is essentially a gradient-projection method, is one of the most popular methods in the SFP literature. In this paper, we revisit the CQ algorithm and give a multi-view on such an algorithm from another four different optimization methods. Specifically, we show that the CQ algorithm can be viewed as applications of partially linearized alternating minimization algorithms, fixed-point methods, DC (Difference-of-Convex) algorithms, and majorization-minimization (MM) algorithms to some structured optimization reformulations of the SFP. Our analysis could provide some new insights into the treatment of SFPs and related topics.

 

How to Cite this Article:
Tingxia Lu, Lulu Zhao, Hongjin He, A multi-view on the CQ algorithm for split feasibility problems: From optimization lens, J. Appl. Numer. Optim. 2 (2020), 387-399.