On the constraints in optimal managing of natural resources systems

Optimal managing of natural resources systems has been permanently in the focus of interest of worldwide policymakers. Today, more than ever, identifying optimal policies is of strategic importance to address the problems crucial to the economy and the environment. Since the beginning of the mathematical programming science the up-to-date mathematical methods were applied to create decision support for natural resources management. However, where the optimal policies have been determined, these often fail. It was shown that this is due to the shortcomings of the models' structure stemming mainly from neglecting of nonlinearities of real systems and miss identification of constraints among relevant variables. This contribution serves as an introductory study of constrained systems arising in the natural resources modeling. We focus on two non-equivalent treatments of such constrained dynamical systems (so called vakonomic and nonholonomic approaches), we discuss the possibility to improve the optimal control models for natural resources systems using nonlinear techniques and, as a test case, we formulate a generalized anti-pollution policy problem.