This chapter will provide a brief introduction to infinite-horizon optimization in discrete time under certainty.

The main purpose of the chapter is to introduce the reader to infinite­horizon optimization techniques and to dynamic programming. These techniques will be used in the rest of the book.

The material in this chapter is presented in four parts. The first part (Sections 6.1­6.3), introduces the problem and provides a number of results necessary for applications of stationary dynamic programming techniques in infinite-dimensional optimization problems. Since understanding how these results are derived is often useful in various applications, the second part, in particular, Sections 6.4 and 6.5, will provide additional tools necessary for a more detailed analysis of dynamic programming and the proofs of the main theorems. The material in these two sections is not necessary for the rest of the book, so that those who only wish to acquire a working knowledge of dynamic programming techniques can skip them. The third part then provides a number of results for nonstationary optimization problems (Section 6.7). Finally, the fourth part of the chapter, consisting of Sections 6.6, 6.8 and 6.9) provides a more detailed discussion of how dynamic programming techniques can be used in applications and also presents a number of results on optimal growth using these tools.

Throughout this chapter, the focus is on discounted maximization problems under cer­tainty, similar to the maximization problems introduced in the previous chapter. Dynamic optimization problems under uncertainty are discussed in Chapter 16.

6.1.