Abstract
This chapter introduces the reader to the basic concepts that form the foundation for the global optimization theoretical developments, methods and applications. In section 2.1 the fundamentals of convex sets are discussed. In section 2.2 the subject of convex and concave functions is presented. In section 2.3 the definitions and properties of quasiconvex and pseudoconvex functions are discussed. Section 2.4 presents the definition and properties of the convex envelopes. Section 2.5 presents the definitions of the local, global optima and E-global optima. Finally, section 2.6 introduces the reader to the basics of difference of convex functions denoted as D.C. functions.
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© 2000 Springer Science+Business Media Dordrecht
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Floudas, C.A. (2000). Basic Concepts of Global Optimization. In: Deterministic Global Optimization. Nonconvex Optimization and Its Applications, vol 37. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-4949-6_2
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DOI: https://doi.org/10.1007/978-1-4757-4949-6_2
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4820-5
Online ISBN: 978-1-4757-4949-6
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