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Strong convergence of a relaxed CQ algorithm for the split feasibility problem

Research paper by Songnian He, Ziyi Zhao

Indexed on: 22 Apr '13Published on: 22 Apr '13Published in: Journal of Inequalities and Applications



Abstract

The split feasibility problem (SFP) is finding a point in a given closed convex subset of a Hilbert space such that its image under a bounded linear operator belongs to a given closed convex subset of another Hilbert space. The most popular iterative method is Byrne’s CQ algorithm. López et al. proposed a relaxed CQ algorithm for solving SFP where the two closed convex sets are both level sets of convex functions. This algorithm can be implemented easily since it computes projections onto half-spaces and has no need to know a priori the norm of the bounded linear operator. However, their algorithm has only weak convergence in the setting of infinite-dimensional Hilbert spaces. In this paper, we introduce a new relaxed CQ algorithm such that the strong convergence is guaranteed. Our result extends and improves the corresponding results of López et al. and some others.MSC:90C25, 90C30, 47J25.