An Approximation Framework for Infinite Horizon Optimization Problems in an Mathematical Programming Setting

Dynamic optimization problems, including optimal control problems, have typically relied on the solution techniques of dynamic programming, involving the sequential solution of certain optimality equations. However, many problems cannot be handled this way, due to complex constraints, a continuous state space, and other complicating factors. When recast as mathematical programs relying on the powerful tools of optimization, especially duality, and decomposability to deal with very large problems, the boundaries imposed by dynamic programming are lifted. This paper develops approximation techniques for stationary infinite horizon problems with discounted costs, in the framework of mathematical programming. A reference is given for parallel results for stochastic dynamic optimization problems.