In recent years, the applications of dynamic optimization procedures in natural resource management have proliferated. A systematic review of these applications is given in terms of a number of optimization methodologies and natural resource systems. Optimization methods are characterized by (1) the mathematical model used to describe a natural resource system, (2) a set of feasible strategies available to the resource manager, and (3) an objective functional by which to measure benefits and costs of strategies. A formal statement of the control problem is used to describe six approaches to optimal utilization of renewable natural resources: variational mathematics, specifically Pontryagin's Maximum Principle; dynamic programming; linear programming; nonlinear programming; simulation-optimization; and classical procedures. Solution methodologies are illustrated for each of these approaches, and examples from the ecological and natural resource literature are described for various subject matter areas. Applications are highlighted in terms of model structures, objective functionals, and system constraints. To the extent possible, optimal management patterns are characterized. Finally, the applicability of the methods to renewable natural resource systems are compared in terms of system complexity, system size, and precision of the optimal solutions. Recommendations are made concerning the appropriate methods for certain kinds of biological resource problems.
