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We examine how to stabilize dynamic programming algorithms by preserving shape.
We improve efficiency by using information about the slope of the value function as well as the level.
Many people use piecewise linear approximations of the value function.
We show how to do that efficiently.We develop the nonlinear programming approach to dynamic programming (DPNLP), using the same basic idea as the linear programming approach but with continuous states and function approximations of the value function.
The DPNLP method can be merged with the MPEC approach to structural estimation to produce computationally efficient empirical methods. Michelangeli’s paper takes this approach.