Optimal harvesting for nonlinear age-dependent population dynamics

• Published in: Mathematical and computer modelling Vol. 43; no. 3; pp. 310 - 319
• Main Authors: Zhao, Chun, Zhao, Ping, Wang, Mian-Sen
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.02.2006; Elsevier Science
• Subjects: Calculus of variations and optimal control; Exact sciences and technology; Global analysis, analysis on manifolds; Mathematical analysis; Mathematics; Optimal control; Optimal harvesting; Partial differential equations; Population dynamics; Sciences and techniques of general use; The maximum principle; The optimal feedback law; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; Optimal harvesting; The maximum principle; Population dynamics; Optimal control; The optimal feedback law; Solution uniqueness; Existence of solution; Maximum principle; Nonlinear problems; Optimal feedback; Necessary condition; Applied mathematics; Variational principle; Optimality condition; Optimal control (mathematics)
• ISSN: 0895-7177; 1872-9479
• DOI: 10.1016/j.mcm.2005.06.008

In this paper, we investigate an optimal harvesting problem for nonlinear age-dependent population dynamics. Using the concept of the normal cone, we also obtain the necessary conditions for optimality for the optimal control problem. Using Ekeland’s variational principle, we demonstrate the existence and uniqueness of solutions for the optimal control problem. Finally, we give the synthesis of the optimal feedback law.