STEADY-STATE POLICIES FOR DETERMINISTIC DYNAMIC PROGRAMS

The heuristic, ″steady state policy, ″for deterministic, stationary dynamic programs is studied, the purpose being to avoid ″curse of dimensionality″ restrictions. Conditions are given under which following that heuristic does not seriously affect the total undiscounted costs over an infinite or a long finite horizon. These include both extensions of our earlier results and entirely new conditions, some of which depend on the saddle-value properties of an associated lagrangian function. Bounds are given on the ″opportunity cost″ (i. e. , the asymptotic difference between the N-stage cost and the optimal N-stage cost) of a certain steady state policy when those conditions hold. These bounds play a useful role in computation. These steady state results are compared with turnpike theorems. Applications include models of ″fractional flows″ and models with convex costs and affine transitions (which typify many economic growth models).