Convex Sets

  • Josef Stoer
  • Christoph Witzgall
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 163)


This chapter surveys the basic properties of convex sets as they will be needed to develop the duality theory of convex programming and to derive saddle point theorems. The material presented is mostly classical: The important separation theorems for convex sets, the existence of supports, Helly’s theorem, and Brouwer’s fixed point theorem (see Bonnesen and Fenchel [1], Eggleston [1], and Fan [7]). In addition, extreme sets are discussed in detail.


Convex Hull Boundary Point Normed Linear Space Relative Interior Supporting Plane 
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Copyright information

© Springer-Verlag Berlin · Heidelberg 1970

Authors and Affiliations

  • Josef Stoer
    • 1
  • Christoph Witzgall
    • 2
  1. 1.Universität WürzburgDeutschland
  2. 2.Boeing Scientific Research LaboratoriesSeattleUSA

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