The multiple-set split feasibility problem and its application in intensity-modulated radiation therapy
170 viewsDOI:
https://doi.org/10.54939/1859-1043.j.mst.FEE.2023.283-288Keywords:
Split common null point problem; Multiple-set split feasibility problem; Intensity-modulated radiation therapy.Abstract
In this paper, we apply a parallel iterative method for solving the split common fixed point problem in Hilbert spaces, without prior knowledge of the transfer operator norm, to the multiple-set split feasibility problem, which plays an important role in medical image reconstruction and signal processing. By formulating a model of the intensity-modulated radiation therapy treatment in a mathematical framework based on the multiple-set split feasibility problem, we also offer an effective approach for solving the intensity-modulated radiation therapy treatment planning.
References
[1]. Byrne C., “Iterative oblique projection onto convex sets and the split feasibility problem”, Inverse Problems 18(2), pp. 441-453, (2002). DOI: https://doi.org/10.1088/0266-5611/18/2/310
[2]. Boikanyo O.A., “A strongly convergent algorithm for the split common fixed point problem”, Appl. Math. Comput. 265 , pp. 844-853, (2015). DOI: https://doi.org/10.1016/j.amc.2015.05.130
[3]. Censor Y., Elfving T., Kopf N., Bortfeld T., “The multiple-sets split feasibility problem and its application”, Inverse Problems 21, pp. 2071-2084, (2005). DOI: https://doi.org/10.1088/0266-5611/21/6/017
[4]. Censor Y., Segal A., “The split common fixed point problem for directed operators”, J. Convex Anal. 16 , pp. 587-600, (2009).
[5]. Cui H., Wang F., “Iterative methods for the split common fixed point problem in Hilbert spaces”, Fixed Point Theory Appl. 2014(1), pp. 1-8, (2014). DOI: https://doi.org/10.1186/1687-1812-2014-78
[6]. Qu B., Liu B., “The split feasibility problem and its solution algorithm”, Math. Probl. Eng. 2018 , pp. 1-7, (2018). DOI: https://doi.org/10.1155/2018/4123168
[7]. Reich S., Tuyen T.M., Trang N.M., “Parallel iterative methods for solving the split common fixed point problem in Hilbert spaces”, Numer. Funct. Anal. Optim. 41(7), pp. 778-805, (2020). DOI: https://doi.org/10.1080/01630563.2019.1681000
