ABSTRACT
A large part of mathematical optimization theory relies on the idea of convex sets (figure 5.1) and convex functions.
Definition 5.1.1 A subset K ⊂ Rn is convex if for all pairs of points X ∈ K,Y ∈ K the line segment joining X and Y is included in K: for all α ∈ [0, 1], αX + (1− α)Y ∈ K.
