A Cyclic and Simultaneous Iterative Method for Solving the Multiple-Sets Split Feasibility Problem

Meng Wen, Jigen Peng and Yuchao Tang ()
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Meng Wen: Xi’an Jiaotong University
Jigen Peng: Xi’an Jiaotong University
Yuchao Tang: NanChang University

Journal of Optimization Theory and Applications, 2015, vol. 166, issue 3, No 8, 844-860

Abstract: Abstract The iterative projection methods for solving the multiple-sets split feasibility problem have been paid much attention in recent years. In this paper, we introduce a cyclic and simultaneous iterative sequence with self-adaptive step size for solving this problem. The advantage of the self-adaptive step size is that it does not need to know the Lipschitz constant of the gradient operator in advance. Furthermore, we propose a relaxed cyclic and simultaneous iterative sequence with self-adaptive step size, respectively. The theoretical convergence results are established in an infinite-dimensional Hilbert spaces setting. Preliminary numerical experiments show that these iteration methods are practical and easy to implement.

Keywords: Multiple-sets split feasibility problem; Cyclic iteration method; Simultaneous iteration method; 90C25; 90C30; 47J25 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-014-0701-9

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