1. An introduction to dynamic optimization-- Optimal Control and Dynamic Programming

Optimization is the unifying paradigm in almost all economic analysis. So before we start, let’s think about optimization. The tree below provides a very nice general representation of the range of optimization problems that you might encounter. There are two things to take from this. First, all optimization problems have a great deal in common: an objective function, constraints, and choice variables. Second, there are lots of different types of optimization problems and how you solve them will depend on the branch on which you find yourself. In terms of the entire tree of all optimization problems, the ones that could be solved analytically would represent a couple of leaves at best – numerical methods must be used to solve the rest. Fortunately, a great deal can be learned about economics by studying those problems that can be solved analytically