Abstract
In this chapter, we present more mathematical background which is necessary for modeling and solution of dynamic transportation network problems. This chapter will cover discrete optimal control, mathematical programming and variational inequality 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 mathematical programming (MP) problems are presented in Section 3.2. Specifically, nonlinear programming (NLP) problems with equality and nonnegativity constraints are presented for comparison. Similarities between discrete optimal control problems and mathematical programming are emphasized.KeywordsVariational InequalityOptimal Control ProblemComplementarity ProblemVariational Inequality ProblemNonlinear Programming ProblemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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