Quaternary Boundary Optimal Control Problem for Quaternary Nonlinear Elliptic System with Constraints
Background: Boundary optimal control problems governed by nonlinear elliptic systems are complex, involving equality and inequality constraints. Objective: This paper examines a quaternary boundary optimal control vector problem (QBOCVP) regulated by a quaternary nonlinear elliptic system (QNES) an...
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Mustansiriyah University
2024-12-01
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| Series: | Al-Mustansiriyah Journal of Science |
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| Online Access: | https://mjs.uomustansiriyah.edu.iq/index.php/MJS/article/view/1546 |
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| author | Alaa S. Khneab Jamil Amir Al-hawasy Ion Chryssoverghi |
| author_facet | Alaa S. Khneab Jamil Amir Al-hawasy Ion Chryssoverghi |
| author_sort | Alaa S. Khneab |
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Background: Boundary optimal control problems governed by nonlinear elliptic systems are complex, involving equality and inequality constraints. Objective: This paper examines a quaternary boundary optimal control vector problem (QBOCVP) regulated by a quaternary nonlinear elliptic system (QNES) and subject to equality and inequality constraints (EINC). Methods: A weak formulation of the QBOCVP is developed, along with a mathematical representation of the quaternary adjoint equations (QAEs) associated with the QNES. Results: An existence theorem for a QBOCV addressing the constrained problem is established and rigorously proven under appropriate assumptions. The QAEs corresponding to the QNES are mathematically formulated. The Fréchet derivative (FD) of the cost function (CF) and the EINC is also derived. Furthermore, the necessary condition theorem (NCTH) and the sufficient condition theorem (SCTH) for optimality are presented and proved. Conclusions: This work provides a rigorous analysis of the QBOCVP with EINC controlled by QNES. It establishes the existence theorem and optimality conditions, providing a theoretical framework for addressing such constrained problems.
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| format | Article |
| id | doaj-art-a8fd9005b467428498dbadbdc2351a56 |
| institution | Kabale University |
| issn | 1814-635X 2521-3520 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Mustansiriyah University |
| record_format | Article |
| series | Al-Mustansiriyah Journal of Science |
| spelling | doaj-art-a8fd9005b467428498dbadbdc2351a562025-01-03T05:01:22ZengMustansiriyah UniversityAl-Mustansiriyah Journal of Science1814-635X2521-35202024-12-0135410.23851/mjs.v35i4.1546Quaternary Boundary Optimal Control Problem for Quaternary Nonlinear Elliptic System with ConstraintsAlaa S. Khneab 0https://orcid.org/0009-0001-8785-4388Jamil Amir Al-hawasy1https://orcid.org/0000-0002-7225-8030Ion Chryssoverghi 2https://orcid.org/0009-0000-8604-3172Karbala Directorate of Education, Karbala, IraqDepartment of Mathematics, College of science, Mustansiriyah University, Baghdad, IraqDepartment of Mathematics, School of Applied Mathematical and Physical Sciences, Athens, Greece Background: Boundary optimal control problems governed by nonlinear elliptic systems are complex, involving equality and inequality constraints. Objective: This paper examines a quaternary boundary optimal control vector problem (QBOCVP) regulated by a quaternary nonlinear elliptic system (QNES) and subject to equality and inequality constraints (EINC). Methods: A weak formulation of the QBOCVP is developed, along with a mathematical representation of the quaternary adjoint equations (QAEs) associated with the QNES. Results: An existence theorem for a QBOCV addressing the constrained problem is established and rigorously proven under appropriate assumptions. The QAEs corresponding to the QNES are mathematically formulated. The Fréchet derivative (FD) of the cost function (CF) and the EINC is also derived. Furthermore, the necessary condition theorem (NCTH) and the sufficient condition theorem (SCTH) for optimality are presented and proved. Conclusions: This work provides a rigorous analysis of the QBOCVP with EINC controlled by QNES. It establishes the existence theorem and optimality conditions, providing a theoretical framework for addressing such constrained problems. https://mjs.uomustansiriyah.edu.iq/index.php/MJS/article/view/1546Fréchet derivativeNecessary and Sufficient Conditions for OptimalityQuaternary Continuous Classical Boundary Optimal Control VectorQuaternary Nonlinear Elliptic System |
| spellingShingle | Alaa S. Khneab Jamil Amir Al-hawasy Ion Chryssoverghi Quaternary Boundary Optimal Control Problem for Quaternary Nonlinear Elliptic System with Constraints Al-Mustansiriyah Journal of Science Fréchet derivative Necessary and Sufficient Conditions for Optimality Quaternary Continuous Classical Boundary Optimal Control Vector Quaternary Nonlinear Elliptic System |
| title | Quaternary Boundary Optimal Control Problem for Quaternary Nonlinear Elliptic System with Constraints |
| title_full | Quaternary Boundary Optimal Control Problem for Quaternary Nonlinear Elliptic System with Constraints |
| title_fullStr | Quaternary Boundary Optimal Control Problem for Quaternary Nonlinear Elliptic System with Constraints |
| title_full_unstemmed | Quaternary Boundary Optimal Control Problem for Quaternary Nonlinear Elliptic System with Constraints |
| title_short | Quaternary Boundary Optimal Control Problem for Quaternary Nonlinear Elliptic System with Constraints |
| title_sort | quaternary boundary optimal control problem for quaternary nonlinear elliptic system with constraints |
| topic | Fréchet derivative Necessary and Sufficient Conditions for Optimality Quaternary Continuous Classical Boundary Optimal Control Vector Quaternary Nonlinear Elliptic System |
| url | https://mjs.uomustansiriyah.edu.iq/index.php/MJS/article/view/1546 |
| work_keys_str_mv | AT alaaskhneab quaternaryboundaryoptimalcontrolproblemforquaternarynonlinearellipticsystemwithconstraints AT jamilamiralhawasy quaternaryboundaryoptimalcontrolproblemforquaternarynonlinearellipticsystemwithconstraints AT ionchryssoverghi quaternaryboundaryoptimalcontrolproblemforquaternarynonlinearellipticsystemwithconstraints |