Maintenance of age-structured populations: Optimal control, state constraints, and bang bang regime
The paper analyzes the optimal maintenance of a "fully manageable" biological population with no natural reproduction. Examples of such populations include dairy farms, horse breeding, gardening, and forestry. Mathematically, the problem leads to the nonlinear optimal control of a first-order partial differential equation with pointwise state constraints. A necessary extremum condition is proven using the abstract optimization theory in Banach spaces. It is shown that the optimal dynamics has a bangbang structure with three jumps and involves buying new young individuals and selling the old ones when their anticipated future expenses exceed the profit. © 2009 World Scientific Publishing Company.
Hritonenko, N., & Yatsenko, Y. (2009). Maintenance of age-structured populations: Optimal control, state constraints, and bang bang regime. Retrieved from https://digitalcommons.pvamu.edu/mathematics-facpubs/61