Existence and uniqueness for the evolutionary impulse control problem using an asynchronous algorithms
Impulse control problems pose significant challenges in decision making under uncertainty, particularly in scenarios where actions must be taken at irregular intervals or in response to abrupt changes in the environment. Ensuring both the existence and uniqueness of optimal control policies in such...
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Elsevier B.V.
2025
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| author | Haiour M. Bencheikh Le Hocine M.E.A. Jan R. Himadan A. Boulaaras S. |
| author2 | 6504628752 |
| author_facet | 6504628752 Haiour M. Bencheikh Le Hocine M.E.A. Jan R. Himadan A. Boulaaras S. |
| author_sort | Haiour M. |
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| collection | Institutional Repository |
| content_provider | Universiti Tenaga Nasional |
| content_source | UNITEN Institutional Repository |
| continent | Asia |
| country | Malaysia |
| description | Impulse control problems pose significant challenges in decision making under uncertainty, particularly in scenarios where actions must be taken at irregular intervals or in response to abrupt changes in the environment. Ensuring both the existence and uniqueness of optimal control policies in such settings is paramount for practical implementation and theoretical understanding. In this study, we investigate the existence and uniqueness of solutions for impulse control problems utilizing asynchronous algorithms. This study presents a novel demonstration concerning the uniqueness and existence of Partially Quasi-Variational Inequalities (PQVIs). Our approach unfolds through a four-step methodology, leveraging distinctive features of a discrete iterative technique. This methodology integrates semi-implicit techniques with respect to the variable t and employs spatial approximation via finite element methods. We establish a pivotal connection between a fixed-point mapping and the discrete EQVIs system, utilizing it to formulate a discrete algorithm featuring a semi-implicit time scheme. Furthermore, we introduce a monotone iterative scheme inspired by Bensoussan's algorithm and rigorously confirm several of its properties through mathematical proofs. This work contributes to advancing the understanding and application of iterative techniques in solving PQVIs, offering insights into their uniqueness and existence. ? 2024 |
| format | Article |
| id | my.uniten.dspace-36470 |
| institution | Universiti Tenaga Nasional |
| publishDate | 2025 |
| publisher | Elsevier B.V. |
| record_format | dspace |
| spelling | my.uniten.dspace-364702025-03-03T15:42:35Z Existence and uniqueness for the evolutionary impulse control problem using an asynchronous algorithms Haiour M. Bencheikh Le Hocine M.E.A. Jan R. Himadan A. Boulaaras S. 6504628752 55582569300 57205596279 57219903927 36994353700 Impulse control problems pose significant challenges in decision making under uncertainty, particularly in scenarios where actions must be taken at irregular intervals or in response to abrupt changes in the environment. Ensuring both the existence and uniqueness of optimal control policies in such settings is paramount for practical implementation and theoretical understanding. In this study, we investigate the existence and uniqueness of solutions for impulse control problems utilizing asynchronous algorithms. This study presents a novel demonstration concerning the uniqueness and existence of Partially Quasi-Variational Inequalities (PQVIs). Our approach unfolds through a four-step methodology, leveraging distinctive features of a discrete iterative technique. This methodology integrates semi-implicit techniques with respect to the variable t and employs spatial approximation via finite element methods. We establish a pivotal connection between a fixed-point mapping and the discrete EQVIs system, utilizing it to formulate a discrete algorithm featuring a semi-implicit time scheme. Furthermore, we introduce a monotone iterative scheme inspired by Bensoussan's algorithm and rigorously confirm several of its properties through mathematical proofs. This work contributes to advancing the understanding and application of iterative techniques in solving PQVIs, offering insights into their uniqueness and existence. ? 2024 Final 2025-03-03T07:42:35Z 2025-03-03T07:42:35Z 2024 Article 10.1016/j.padiff.2024.100766 2-s2.0-85196321855 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85196321855&doi=10.1016%2fj.padiff.2024.100766&partnerID=40&md5=fdab7c7d659c806342a6bfde05ec6d99 https://irepository.uniten.edu.my/handle/123456789/36470 11 100766 All Open Access; Gold Open Access Elsevier B.V. Scopus |
| spellingShingle | Haiour M. Bencheikh Le Hocine M.E.A. Jan R. Himadan A. Boulaaras S. Existence and uniqueness for the evolutionary impulse control problem using an asynchronous algorithms |
| title | Existence and uniqueness for the evolutionary impulse control problem using an asynchronous algorithms |
| title_full | Existence and uniqueness for the evolutionary impulse control problem using an asynchronous algorithms |
| title_fullStr | Existence and uniqueness for the evolutionary impulse control problem using an asynchronous algorithms |
| title_full_unstemmed | Existence and uniqueness for the evolutionary impulse control problem using an asynchronous algorithms |
| title_short | Existence and uniqueness for the evolutionary impulse control problem using an asynchronous algorithms |
| title_sort | existence and uniqueness for the evolutionary impulse control problem using an asynchronous algorithms |
| url_provider | http://dspace.uniten.edu.my/ |