Algorithm for Solutions of Nonlinear Equations of Strongly Monotone Type and Applications to Convex Minimization and Variational Inequality Problems
Real-life problems are governed by equations which are nonlinear in nature. Nonlinear equations occur in modeling problems, such as minimizing costs in industries and minimizing risks in businesses. A technique which does not involve the assumption of existence of a real constant whose calculation i...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2020/6579720 |
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| _version_ | 1832546838067019776 |
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| author | Mathew O. Aibinu Surendra C. Thakur Sibusiso Moyo |
| author_facet | Mathew O. Aibinu Surendra C. Thakur Sibusiso Moyo |
| author_sort | Mathew O. Aibinu |
| collection | DOAJ |
| description | Real-life problems are governed by equations which are nonlinear in nature. Nonlinear equations occur in modeling problems, such as minimizing costs in industries and minimizing risks in businesses. A technique which does not involve the assumption of existence of a real constant whose calculation is unclear is used to obtain a strong convergence result for nonlinear equations of p,η-strongly monotone type, where η>0,p>1. An example is presented for the nonlinear equations of p,η-strongly monotone type. As a consequence of the main result, the solutions of convex minimization and variational inequality problems are obtained. This solution has applications in other fields such as engineering, physics, biology, chemistry, economics, and game theory. |
| format | Article |
| id | doaj-art-d549c0de2e4944d38f1c988bdd2d5078 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d549c0de2e4944d38f1c988bdd2d50782025-02-03T06:46:55ZengWileyAbstract and Applied Analysis1085-33751687-04092020-01-01202010.1155/2020/65797206579720Algorithm for Solutions of Nonlinear Equations of Strongly Monotone Type and Applications to Convex Minimization and Variational Inequality ProblemsMathew O. Aibinu0Surendra C. Thakur1Sibusiso Moyo2Institute for Systems Science & KZN CoLab, Durban University of Technology, Durban 4000, South AfricaKZN CoLab, Durban University of Technology, Durban 4000, South AfricaInstitute for Systems Science & Office of the DVC Research, Innovation & Engagement Milena Court, Durban University of Technology, Durban 4000, South AfricaReal-life problems are governed by equations which are nonlinear in nature. Nonlinear equations occur in modeling problems, such as minimizing costs in industries and minimizing risks in businesses. A technique which does not involve the assumption of existence of a real constant whose calculation is unclear is used to obtain a strong convergence result for nonlinear equations of p,η-strongly monotone type, where η>0,p>1. An example is presented for the nonlinear equations of p,η-strongly monotone type. As a consequence of the main result, the solutions of convex minimization and variational inequality problems are obtained. This solution has applications in other fields such as engineering, physics, biology, chemistry, economics, and game theory.http://dx.doi.org/10.1155/2020/6579720 |
| spellingShingle | Mathew O. Aibinu Surendra C. Thakur Sibusiso Moyo Algorithm for Solutions of Nonlinear Equations of Strongly Monotone Type and Applications to Convex Minimization and Variational Inequality Problems Abstract and Applied Analysis |
| title | Algorithm for Solutions of Nonlinear Equations of Strongly Monotone Type and Applications to Convex Minimization and Variational Inequality Problems |
| title_full | Algorithm for Solutions of Nonlinear Equations of Strongly Monotone Type and Applications to Convex Minimization and Variational Inequality Problems |
| title_fullStr | Algorithm for Solutions of Nonlinear Equations of Strongly Monotone Type and Applications to Convex Minimization and Variational Inequality Problems |
| title_full_unstemmed | Algorithm for Solutions of Nonlinear Equations of Strongly Monotone Type and Applications to Convex Minimization and Variational Inequality Problems |
| title_short | Algorithm for Solutions of Nonlinear Equations of Strongly Monotone Type and Applications to Convex Minimization and Variational Inequality Problems |
| title_sort | algorithm for solutions of nonlinear equations of strongly monotone type and applications to convex minimization and variational inequality problems |
| url | http://dx.doi.org/10.1155/2020/6579720 |
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