Convex Analysis and Set-Valued Maps: A Review

Part of the Springer Monographs in Mathematics book series (SMM)


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.


Convex Function Convex Cone Normal Cone Support Function Convex Analysis 
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© Springer-Verlag New York, Inc. 2003

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