Abstract
In this chapter, we present more mathematical background which is necessary for modeling and solving dynamic transportation network problems. This chapter covers discrete optimal control and nonlinear programming problems. First, we introduce the discrete optimal control problem (OCP). To simplify our presentation, we consider discrete optimal control problems with fixed end times as examples in Section 3.1. The discussion is focused on the analysis of optimality conditions. Then, some nonlinear programming (NLP) problems with equality and nonnegativity constraints are presented in Section 3.2. Similarities between discrete optimal control and nonlinear programming are emphasized.
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