Chapter 4 - One-dimensional Dynamic Programming: Analytic Solutions

Abstract

This chapter focuses on the principles of dynamic programming to a large number of mathematical problems that have one thing in common, namely, in the expressions for the recursion relations, the maximization or minimization can be performed without recourse to numerical tabulation of the stage returns and the optimal return functions. Instead, the optimal return functions, gs(λs) can be represented by a mathematical formula and, indeed, classical optimization methods can be employed to obtain these representations. There are many activities where it makes sense to consider minimizing a maximum value of some measure rather than a pure minimization of some objective. The chapter discusses a problem in which a concave function was minimized over a closed convex set in each of the one-dimensional subproblems.