Bounded Perturbation Resilience of Two Modified Relaxed CQ Algorithms for the Multiple-Sets Split Feasibility Problem
In this paper, we present some modified relaxed CQ algorithms with different kinds of step size and perturbation to solve the Multiple-sets Split Feasibility Problem (MSSFP). Under mild assumptions, we establish weak convergence and prove the bounded perturbation resilience of the proposed algorithm...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-08-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/10/3/197 |
| _version_ | 1797520187903180800 |
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| author | Yingying Li Yaxuan Zhang |
| author_facet | Yingying Li Yaxuan Zhang |
| author_sort | Yingying Li |
| collection | DOAJ |
| description | In this paper, we present some modified relaxed CQ algorithms with different kinds of step size and perturbation to solve the Multiple-sets Split Feasibility Problem (MSSFP). Under mild assumptions, we establish weak convergence and prove the bounded perturbation resilience of the proposed algorithms in Hilbert spaces. Treating appropriate inertial terms as bounded perturbations, we construct the inertial acceleration versions of the corresponding algorithms. Finally, for the LASSO problem and three experimental examples, numerical computations are given to demonstrate the efficiency of the proposed algorithms and the validity of the inertial perturbation. |
| first_indexed | 2024-03-10T07:53:18Z |
| format | Article |
| id | doaj.art-733b7a2731bc432c9f5950485ff4e270 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T07:53:18Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-733b7a2731bc432c9f5950485ff4e2702023-11-22T12:02:50ZengMDPI AGAxioms2075-16802021-08-0110319710.3390/axioms10030197Bounded Perturbation Resilience of Two Modified Relaxed CQ Algorithms for the Multiple-Sets Split Feasibility ProblemYingying Li0Yaxuan Zhang1College of Science, Civil Aviation University of China, Tianjin 300300, ChinaCollege of Science, Civil Aviation University of China, Tianjin 300300, ChinaIn this paper, we present some modified relaxed CQ algorithms with different kinds of step size and perturbation to solve the Multiple-sets Split Feasibility Problem (MSSFP). Under mild assumptions, we establish weak convergence and prove the bounded perturbation resilience of the proposed algorithms in Hilbert spaces. Treating appropriate inertial terms as bounded perturbations, we construct the inertial acceleration versions of the corresponding algorithms. Finally, for the LASSO problem and three experimental examples, numerical computations are given to demonstrate the efficiency of the proposed algorithms and the validity of the inertial perturbation.https://www.mdpi.com/2075-1680/10/3/197multiple-sets split feasibility problemCQ algorithmbounded perturbationarmijo-line searchself-adaptive step size |
| spellingShingle | Yingying Li Yaxuan Zhang Bounded Perturbation Resilience of Two Modified Relaxed CQ Algorithms for the Multiple-Sets Split Feasibility Problem Axioms multiple-sets split feasibility problem CQ algorithm bounded perturbation armijo-line search self-adaptive step size |
| title | Bounded Perturbation Resilience of Two Modified Relaxed CQ Algorithms for the Multiple-Sets Split Feasibility Problem |
| title_full | Bounded Perturbation Resilience of Two Modified Relaxed CQ Algorithms for the Multiple-Sets Split Feasibility Problem |
| title_fullStr | Bounded Perturbation Resilience of Two Modified Relaxed CQ Algorithms for the Multiple-Sets Split Feasibility Problem |
| title_full_unstemmed | Bounded Perturbation Resilience of Two Modified Relaxed CQ Algorithms for the Multiple-Sets Split Feasibility Problem |
| title_short | Bounded Perturbation Resilience of Two Modified Relaxed CQ Algorithms for the Multiple-Sets Split Feasibility Problem |
| title_sort | bounded perturbation resilience of two modified relaxed cq algorithms for the multiple sets split feasibility problem |
| topic | multiple-sets split feasibility problem CQ algorithm bounded perturbation armijo-line search self-adaptive step size |
| url | https://www.mdpi.com/2075-1680/10/3/197 |
| work_keys_str_mv | AT yingyingli boundedperturbationresilienceoftwomodifiedrelaxedcqalgorithmsforthemultiplesetssplitfeasibilityproblem AT yaxuanzhang boundedperturbationresilienceoftwomodifiedrelaxedcqalgorithmsforthemultiplesetssplitfeasibilityproblem |