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October, 2022 A Parallel Algorithm for Generalized Multiple-set Split Feasibility with Application to Optimal Control Problems
Nguyen Thi Thu Thuy, Nguyen Trung Nghia
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Taiwanese J. Math. 26(5): 1069-1092 (October, 2022). DOI: 10.11650/tjm/220502

Abstract

In this paper, we concentrate on the generalized multiple-set split feasibility problems in Hilbert spaces and propose a new iterative method for this problem. One of the most important of this method is using dynamic step-sizes, in which the information of the previous step is the only requirement to compute the next approximation. The strong convergence result of the suggested algorithm is proven theoretically under some feasible assumptions. When considering the main results in some special cases, we also obtain some applications regarding the solution of the multiple-set split feasibility problem, the split feasibility problem with multiple output sets, and the split feasibility problem as well as the linear optimal control problem. Some numerical experiments on infinite-dimensional spaces and applications in optimal control problems are conducted to demonstrate the advantages and computational efficiency of the proposed algorithms over some existing results.

Funding Statement

The first author was supported by the Science and Technology Fund of the Vietnam Ministry of Education and Training (B2022–BKA–02).

Acknowledgments

The authors would like to thank the referees for their valuable comments and suggestions which improve the presentation of this manuscript.

Citation

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Nguyen Thi Thu Thuy. Nguyen Trung Nghia. "A Parallel Algorithm for Generalized Multiple-set Split Feasibility with Application to Optimal Control Problems." Taiwanese J. Math. 26 (5) 1069 - 1092, October, 2022. https://doi.org/10.11650/tjm/220502

Information

Received: 6 December 2021; Revised: 9 March 2022; Accepted: 16 May 2022; Published: October, 2022
First available in Project Euclid: 26 May 2022

Digital Object Identifier: 10.11650/tjm/220502

Subjects:
Primary: 41A65 , 47H05 , 47H09 , 49J53 , 90C25

Keywords: discrete optimal control problems , multiple-set problems , parallel algorithm , split feasibility problems

Rights: Copyright © 2022 The Mathematical Society of the Republic of China

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Vol.26 • No. 5 • October, 2022
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