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Reading Notes on Chapter 2

Reading Notes on Chapter 2

In the front of this chapter, defining some concepts of mathematical such as, convex set, affine function, etc. For more detail about these, please referring to Wiki.

2.1 Mathematical background: convex optimization

2.1.1 Convex sets and convex functions

Definition 2.1.1 (Convex set) 

A set S ⊆ R^n is convex if ax+(1-a)y ∈ S whenever x,y ∈S and a ∈[0,1]. Since ax+(1-a)y, for a ∈[0,1], describes the line segment between x and y, a convex set can be pictorially depicted as Figure 2.1: given any two points x,y ∈ S, the line segment between x and y lies entirely in S.

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