Dynamic Programming

Abstract In Chapter 10 we studied optimization over time. The constraints (10.1) expressing increments to stocks or state variables, and the additively separable form (10.3) of the objective function, were special features that enabled us to express the first-order conditions in a useful special form, namely as the Maximum Principle. Dynamic Programming is an alternative way of solving the same problem. It proves especially useful when time and uncertainty appear together, as they so often do in reality. Let us begin with time to keep the exposition simple, and introduce uncertainty later. subject to the constraints