Modified Relaxed CQ Iterative Algorithms for the Split Feasibility Problem

Xinglong Wang, Jing Zhao and Dingfang Hou
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Xinglong Wang: College of Air Traffic Management, Civil Aviation University of China, Tianjin 300300, China
Jing Zhao: College of Science, Civil Aviation University of China, Tianjin 300300, China
Dingfang Hou: College of Science, Civil Aviation University of China, Tianjin 300300, China

Mathematics, 2019, vol. 7, issue 2, 1-17

Abstract: The split feasibility problem models inverse problems arising from phase retrievals problems and intensity-modulated radiation therapy. For solving the split feasibility problem, Xu proposed a relaxed CQ algorithm that only involves projections onto half-spaces. In this paper, we use the dual variable to propose a new relaxed CQ iterative algorithm that generalizes Xu’s relaxed CQ algorithm in real Hilbert spaces. By using projections onto half-spaces instead of those onto closed convex sets, the proposed algorithm is implementable. Moreover, we present modified relaxed CQ algorithm with viscosity approximation method. Under suitable conditions, global weak and strong convergence of the proposed algorithms are proved. Some numerical experiments are also presented to illustrate the effectiveness of the proposed algorithms. Our results improve and extend the corresponding results of Xu and some others.

Keywords: split feasibility problem; relaxed CQ algorithm; convergence; Hilbert space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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