Abstract
Convexity plays a fundamental role in the analysis of optimization problems. In this very brief chapter we review some basic concepts on convex sets and convex functions. The material is presented quickly with no proofs and should be familiar to a reader who has had a standard convex analysis course. Some of the topics that might be less familiar and particularly relevant to this monograph will be given in greater details. Similarly, we review the basic definitions and properties of set-valued maps.
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© 2003 Springer-Verlag New York, Inc.
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(2003). Convex Analysis and Set-Valued Maps: A Review. In: Asymptotic Cones and Functions in Optimization and Variational Inequalities. Springer Monographs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/0-387-22590-0_1
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DOI: https://doi.org/10.1007/0-387-22590-0_1
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-95520-9
Online ISBN: 978-0-387-22590-6
eBook Packages: Springer Book Archive