Convex sets play a very important role in geometry. In this chapter, we state some of the “classics” of convex affine geometry: Carathéodory's Theorem, Radon's ...
Note: A convex set can be defined by the property that any convex combination of two points from the set is also in the set. Theorem: Let C ⊆ Rn be a convex ...
In geometry, a subset of a Euclidean space, or more generally an affine space over the reals, is convex if, given any two points in the subset, the subset ...
Convex Optimization. Boyd and Vandenberghe. 2.12. Page 15. Intersection. ▷ the intersection of (any number of) convex sets is convex. ▷ example: – S = x ∈ ...
We cover the definition and properties of convex sets and functions, and provide a toolkit of techniques to prove convexity. We will later use these techniques ...