Discrete Optimal Control Method Based on the Optimal Strategy of Fishing
Consideration was given to the discrete optimal control method for the optimal fishing strategy. Our method is new and efficient for discrete optimal control problem, which is different from the other optimal methods such as the traditional variational method, the Pontryagin principle of maximum, an...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/727531 |
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| _version_ | 1849304755624476672 |
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| author | Lichun Zhang Qingdao Huang |
| author_facet | Lichun Zhang Qingdao Huang |
| author_sort | Lichun Zhang |
| collection | DOAJ |
| description | Consideration was given to the discrete optimal control method for the optimal fishing strategy. Our method is new and efficient for discrete optimal control problem, which is different from the other optimal methods such as the traditional variational method, the Pontryagin principle of maximum, and the dynamic programming. The basic construction of the model is the traditional logistic function relating to the growth of fry. The discrete optimal control method for optimal fishing strategy was used to construct the optimal rate of each fishing strategy; the main focus of our work is on the rigorous mathematical analysis of the optimal control problem. The analysis allows one to obtain the optimal initial investment amount of the fry and the optimal size of the total catch. Furthermore, when the initial investment amount of the fry is below or above the optimal value and the intrinsic growth rate of fish R is too small, we derive that fishing operations should not be started in the last few years to make the overall fishing amount optimal. At last, several typical examples are given to illustrate the obtained results. |
| format | Article |
| id | doaj-art-3df783ac2ca242f6b273cf4ec52f476b |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-3df783ac2ca242f6b273cf4ec52f476b2025-08-20T03:55:40ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/727531727531Discrete Optimal Control Method Based on the Optimal Strategy of FishingLichun Zhang0Qingdao Huang1Mathematics School and Institute, Jilin University, Changchun, Jilin 130012, ChinaMathematics School and Institute, Jilin University, Changchun, Jilin 130012, ChinaConsideration was given to the discrete optimal control method for the optimal fishing strategy. Our method is new and efficient for discrete optimal control problem, which is different from the other optimal methods such as the traditional variational method, the Pontryagin principle of maximum, and the dynamic programming. The basic construction of the model is the traditional logistic function relating to the growth of fry. The discrete optimal control method for optimal fishing strategy was used to construct the optimal rate of each fishing strategy; the main focus of our work is on the rigorous mathematical analysis of the optimal control problem. The analysis allows one to obtain the optimal initial investment amount of the fry and the optimal size of the total catch. Furthermore, when the initial investment amount of the fry is below or above the optimal value and the intrinsic growth rate of fish R is too small, we derive that fishing operations should not be started in the last few years to make the overall fishing amount optimal. At last, several typical examples are given to illustrate the obtained results.http://dx.doi.org/10.1155/2015/727531 |
| spellingShingle | Lichun Zhang Qingdao Huang Discrete Optimal Control Method Based on the Optimal Strategy of Fishing Discrete Dynamics in Nature and Society |
| title | Discrete Optimal Control Method Based on the Optimal Strategy of Fishing |
| title_full | Discrete Optimal Control Method Based on the Optimal Strategy of Fishing |
| title_fullStr | Discrete Optimal Control Method Based on the Optimal Strategy of Fishing |
| title_full_unstemmed | Discrete Optimal Control Method Based on the Optimal Strategy of Fishing |
| title_short | Discrete Optimal Control Method Based on the Optimal Strategy of Fishing |
| title_sort | discrete optimal control method based on the optimal strategy of fishing |
| url | http://dx.doi.org/10.1155/2015/727531 |
| work_keys_str_mv | AT lichunzhang discreteoptimalcontrolmethodbasedontheoptimalstrategyoffishing AT qingdaohuang discreteoptimalcontrolmethodbasedontheoptimalstrategyoffishing |