Nonlinear Programming and Discrete-Time Optimal Control

Terry L. Friesz ()
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Terry L. Friesz: Pennsylvania State University

Chapter Chapter 2 in Dynamic Optimization and Differential Games, 2010, pp 33-78 from Springer

Abstract: Abstract The primary intent of this chapter is to introduce the reader to the theoretical foundations of nonlinear programming as well as the theoretical foundations of deterministic discrete-time optimal control. In fact, deterministic discrete-time optimal control problems, as we shall see, are actually nonlinear mathematical programs with a very particular type of structure. In a later chapter, we will also discover that deterministic continuous-time optimal control problems are specific instances of mathematical programs in topological vector spaces. Consequently, it is imperative for the student of optimal control to have a command of the foundations of nonlinear programming. Particularly important are the notions of local and global optimality in mathematical programming, the Kuhn-Tucker necessary conditions for optimality in nonlinear programming, and the role played by convexity in making necessary conditions sufficient. Readers already comfortable with finite-dimensional nonlinear programming may wish to go immediately to Section 2.9. We do caution, however, that subsequent chapters of this book assume substantial familiarity with finite-dimensional nonlinear programming, so that an overestimate of one’s nonlinear programming knowledge can be very detrimental to ultimately obtaining a deep understanding of optimal control theory and differential games.

Keywords: Mathematical Program; Nonlinear Programming; Inequality Constraint; Optimal Control Theory; Unconstrained Minimum (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-0-387-72778-3_2

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