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Erschienen in:
2012 | OriginalPaper | Buchkapitel
Principles and basic concepts
verfasst von : Daniel Scholz
Erschienen in: Deterministic Global Optimization
Verlag: Springer New York
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In this chapter, our main goal is to summarize principles and basic concepts that are of fundamental importance in the remainder of this text, especially in Chapter 3 where bounding operations are presented.We begin with the definition of convex functions and some generalizations of convexity in Section 1.1. Some fundamental but important results are given before we discuss subgradients. Next, in Section 1.2 we briefly introduce distance measures given by norms. Distance measures are quite important in the subsequent Section 1.3 where we give a very brief introduction to location theory. Furthermore, we show how to solve theWeber problem for the rectilinear and Euclidean norms. Moreover, d.c. functions are introduced in Section 1.4 and basic properties are collected. Finally, we give an introduction to interval analysis in Section 1.5 which leads to several bounding operations later on.