Linear Convergence of an Iterative Algorithm for Solving the Multiple-Sets Split Feasibility Problem

Tingting Tian, Luoyi Shi and Rudong Chen
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Tingting Tian: Department of Mathematical Science, Tianjin Polytechnic University, Tianjin 300387, China
Luoyi Shi: Department of Mathematical Science, Tianjin Polytechnic University, Tianjin 300387, China
Rudong Chen: Department of Mathematical Science, Tianjin Polytechnic University, Tianjin 300387, China

Mathematics, 2019, vol. 7, issue 7, 1-13

Abstract: In this paper, we propose the simultaneous sub-gradient projection algorithm with the dynamic step size (SSPA for short) for solving the multiple-sets split feasibility problem (MSSFP for short) and investigate its linear convergence. We involve a notion of bounded linear regularity for the MSSFP and construct several sufficient conditions to prove the linear convergence for the SSPA. In particular, the SSPA is an easily calculated algorithm that uses orthogonal projection onto half-spaces. Furthermore, some numerical results are provided to verify the effectiveness of our proposed algorithm.

Keywords: linear convergence; bounded linear regularity; multiple-sets split feasibility problem; simultaneous sub-gradient projection algorithm with the dynamic step size (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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