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Open AccessArticle

Gradient Methods with Selection Technique for the Multiple-Sets Split Equality Problem

1
School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China
2
Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(10), 928; https://doi.org/10.3390/math7100928
Received: 17 August 2019 / Revised: 26 September 2019 / Accepted: 26 September 2019 / Published: 8 October 2019
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications)
The inverse problem is one of the four major problems in computational mathematics. There is an inverse problem in medical image reconstruction and radiotherapy that is called the multiple-sets split equality problem. The multiple-sets split equality problem is a unified form of the split feasibility problem, split equality problem, and split common fixed point problem. In this paper, we present two iterative algorithms for solving it. The suggested algorithms are based on the gradient method with a selection technique. Based on this technique, we only need to calculate one projection in each iteration. View Full-Text
Keywords: multiple-sets split equality problem; split equality problem; selection technique multiple-sets split equality problem; split equality problem; selection technique
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Tian, D.; Jiang, L.; Shi, L. Gradient Methods with Selection Technique for the Multiple-Sets Split Equality Problem. Mathematics 2019, 7, 928.

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