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 , Eggleston , and Fan ). In addition, extreme sets are discussed in detail.
KeywordsConvex Hull Boundary Point Normed Linear Space Relative Interior Supporting Plane
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