On Constraint Sampling in the Linear Programming Approach to Approximate Dynamic Programming
Mathematics of Operations Research
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Dynamic programming problems are common in economics, finance and natural resource management. However, exact solutions to these problems are exceptional. Instead, solutions typically rely on numerical approximation techniques which vary in use, complexity and computational requirements. Perturbation, projection and linear programming approaches are among the most useful of these numerical techniques. In this paper, we extend the parametric linear programming technique to include continuous-time problems with jump-diffusion processes, and compare it to projection and perturbation techniques for solving dynamic programming problems in terms of computational speed, accuracy, ease of use and scope. The comparisons are drawn from solutions to two fisheries management problems - a unidimensional model of optimal harvest and a multidimensional model for optimal marine reserve size. Available computer code illustrates how each technique solves these problems and how they can be applied to other comparable problems in natural resource modelling.