Optimal Harvesting for Size-Dependent Control

Abstract

We investigate some optimal harvesting problems concerning the age-structured population dynamics. The goal is to maximize the profit with respect to a size-dependent harvesting effort. The harvesting is made either by fishing or by hunting. For each studied problem, we state the necessary optimality conditions and use them to get the structure of the optimal control. For the problem related to hunting, we derive an iterative algorithm to improve at each step the harvesting effort, in order to increase the profit. Numerical tests are performed to show that the proposed methods are effective.