Optimal harvesting control problem for linear periodic age-dependent population dynamics

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• 作者：Luo ; Zhixue ; Li ; Wan-Tong ; Wang ; Miansen
• 关键词：Optimal harvesting ; Optimal control ; Periodic population dynamics ; The maximum principle
• 刊名：Applied Mathematics and Computation
• 出版年：2004
• 期刊代码：7_00963003
• 类别：cp
• 出版时间：April 15, 2004
• 卷：151
• 期：3
• 页码：789-800
• 文件大小：223 K

摘要

In this paper, we investigate an optimal harvesting problem for linear periodic age-dependent population dynamics. Namely, we consider the Lotka–Mckendrick model with periodic vital rates and a periodic forcing term that sustains oscillations. By Mazur's Theorem, we demonstrate existence of solutions of the optimal control problem (OH) and by the conception of normal cone, we also obtain the first order necessary conditions of optimality for problem (OH). Finally, under suitable assumptions, we give uniqueness of solutions of the optimal control problem (OH). Our results extend some known criteria.