A Dai-Liao-type projection method for monotone nonlinear equations and signal processing
In this article, inspired by the projection technique of Solodov and Svaiter, we exploit the simple structure, low memory requirement, and good convergence properties of the mixed conjugate gradient method of Stanimirović et al. [New hybrid conjugate gradient and broyden-fletcher-goldfarbshanno conj...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2022-12-01
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| Series: | Demonstratio Mathematica |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/dema-2022-0159 |
| _version_ | 1827347417309118464 |
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| author | Ibrahim Abdulkarim Hassan Kumam Poom Abubakar Auwal Bala Abdullahi Muhammad Sirajo Mohammad Hassan |
| author_facet | Ibrahim Abdulkarim Hassan Kumam Poom Abubakar Auwal Bala Abdullahi Muhammad Sirajo Mohammad Hassan |
| author_sort | Ibrahim Abdulkarim Hassan |
| collection | DOAJ |
| description | In this article, inspired by the projection technique of Solodov and Svaiter, we exploit the simple structure, low memory requirement, and good convergence properties of the mixed conjugate gradient method of Stanimirović et al. [New hybrid conjugate gradient and broyden-fletcher-goldfarbshanno conjugate gradient methods, J. Optim. Theory Appl. 178 (2018), no. 3, 860–884] for unconstrained optimization problems to solve convex constrained monotone nonlinear equations. The proposed method does not require Jacobian information. Under monotonicity and Lipschitz continuity assumptions, the global convergence properties of the proposed method are established. Computational experiments indicate that the proposed method is computationally efficient. Furthermore, the proposed method is applied to solve the ℓ1{\ell }_{1}-norm regularized problems to decode sparse signals and images in compressive sensing. |
| first_indexed | 2024-03-07T23:49:19Z |
| format | Article |
| id | doaj.art-91279d5acb4e465dbd4aac0b95d57209 |
| institution | Directory Open Access Journal |
| issn | 2391-4661 |
| language | English |
| last_indexed | 2024-03-07T23:49:19Z |
| publishDate | 2022-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj.art-91279d5acb4e465dbd4aac0b95d572092024-02-19T09:01:34ZengDe GruyterDemonstratio Mathematica2391-46612022-12-01551978101310.1515/dema-2022-0159A Dai-Liao-type projection method for monotone nonlinear equations and signal processingIbrahim Abdulkarim Hassan0Kumam Poom1Abubakar Auwal Bala2Abdullahi Muhammad Sirajo3Mohammad Hassan4Center of Excellence in Theoretical and Computational Science (TaCS-CoE), SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, ThailandCenter of Excellence in Theoretical and Computational Science (TaCS-CoE), SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, ThailandDepartment of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, Pretoria, Medunsa-0204, South AfricaDepartment of Mathematics, Usmanu Danfodiyo University, Sokoto, NigeriaDepartment of Mathematical Sciences, Faculty of Physical Sciences, Bayero University, Kano. Kano, NigeriaIn this article, inspired by the projection technique of Solodov and Svaiter, we exploit the simple structure, low memory requirement, and good convergence properties of the mixed conjugate gradient method of Stanimirović et al. [New hybrid conjugate gradient and broyden-fletcher-goldfarbshanno conjugate gradient methods, J. Optim. Theory Appl. 178 (2018), no. 3, 860–884] for unconstrained optimization problems to solve convex constrained monotone nonlinear equations. The proposed method does not require Jacobian information. Under monotonicity and Lipschitz continuity assumptions, the global convergence properties of the proposed method are established. Computational experiments indicate that the proposed method is computationally efficient. Furthermore, the proposed method is applied to solve the ℓ1{\ell }_{1}-norm regularized problems to decode sparse signals and images in compressive sensing.https://doi.org/10.1515/dema-2022-0159nonlinear equationsunconstrained optimizationconjugate gradient methodprojection methodcompressive sensing90c3065k0590c5349m3715a18 |
| spellingShingle | Ibrahim Abdulkarim Hassan Kumam Poom Abubakar Auwal Bala Abdullahi Muhammad Sirajo Mohammad Hassan A Dai-Liao-type projection method for monotone nonlinear equations and signal processing Demonstratio Mathematica nonlinear equations unconstrained optimization conjugate gradient method projection method compressive sensing 90c30 65k05 90c53 49m37 15a18 |
| title | A Dai-Liao-type projection method for monotone nonlinear equations and signal processing |
| title_full | A Dai-Liao-type projection method for monotone nonlinear equations and signal processing |
| title_fullStr | A Dai-Liao-type projection method for monotone nonlinear equations and signal processing |
| title_full_unstemmed | A Dai-Liao-type projection method for monotone nonlinear equations and signal processing |
| title_short | A Dai-Liao-type projection method for monotone nonlinear equations and signal processing |
| title_sort | dai liao type projection method for monotone nonlinear equations and signal processing |
| topic | nonlinear equations unconstrained optimization conjugate gradient method projection method compressive sensing 90c30 65k05 90c53 49m37 15a18 |
| url | https://doi.org/10.1515/dema-2022-0159 |
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