Half-Space Relaxation Projection Method for Solving Multiple-Set Split Feasibility Problem
<span>In this paper, we study an iterative method for solving the multiple-set split feasibility<br />problem: find a point in the intersection of a finite family of closed convex sets in one space such<br />that its image under a linear transformation belongs to the intersection o...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2020-07-01
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| Series: | Mathematical and Computational Applications |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2297-8747/25/3/47 |
| Summary: | <span>In this paper, we study an iterative method for solving the multiple-set split feasibility<br />problem: find a point in the intersection of a finite family of closed convex sets in one space such<br />that its image under a linear transformation belongs to the intersection of another finite family of<br />closed convex sets in the image space. In our result, we obtain a strongly convergent algorithm by<br />relaxing the closed convex sets to half-spaces, using the projection onto those half-spaces and by<br />introducing the extended form of selecting step sizes used in a relaxed CQ algorithm for solving the<br />split feasibility problem. We also give several numerical examples for illustrating the efficiency and<br />implementation of our algorithm in comparison with existing algorithms in the literature.</span> |
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| ISSN: | 1300-686X 2297-8747 |