The Split Feasibility Problem in Hilbert Space

Wu, Dingping; Duan, Qibin; Erli, Wang; Zhao, Hang

doi:10.1007/978-3-642-31698-2_161

Cited by 1 publication

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“…A variety of algorithms have been proposed for solving the linear split feasibility problem notably those in image reconstruction and intensity-modulated radiation therapy (IMRT) [6,10,12,14,47]. The split feasibility problem has been studied in more general settings, for example in infinite dimensions [21,37,48] and within the broader context of split inverse problems [13].…”

Section: Introductionmentioning

confidence: 99%

An MM Algorithm for Split Feasibility Problems

Xu,

Chi,

Yang

et al. 2016

Preprint

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The classical multi-set split feasibility problem seeks a point in the intersection of finitely many closed convex domain constraints, whose image under a linear mapping also lies in the intersection of finitely many closed convex range constraints. Split feasibility generalizes important inverse problems including convex feasibility, linear complementarity, and regression with constraint sets. When a feasible point does not exist, solution methods that proceed by minimizing a proximity function can be used to obtain optimal approximate solutions to the problem. We present an extension of the proximity function approach that generalizes the linear split feasibility problem to allow for non-linear mappings. Our algorithm is based on the principle of majorization-minimization, is amenable to quasi-Newton acceleration, and comes complete with convergence guarantees under mild assumptions. Furthermore, we show that the Euclidean norm appearing in the proximity function of the non-linear split feasibility problem can be replaced by arbitrary Bregman divergences. We explore several examples illustrating the merits of

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