A polyhederal approximation approach to concave numerical dynamic programming

This paper describes a method for solving concave numerical dynamic programming problems which is based a pair of polyhederal approximations of concave functions. The method is robust in that (i) it is globally convergent, (ii) it produces exact error bounds on the computed value function which can in theory be made arbitrarily tight, and (iii) its implementation boils down to solving a sequence of linear programs. This is true regardless of the dimensionality of the state space, the pattern of binding constraints, and the smoothness of model primitives. Numerical examples suggest that the method is capable of producing accurate solutions in an ecient manner.