Convex sets

In this chapter, a variety of convex sets and related definitions are described.

Affine set

Suppose x_1, x_2 are two points in \mathbb{R^n}. Then the line passing through them is defined as follows:

Convex set

Suppose x_1, x_2 are two points in \mathbb{R^n}. Then the line segment between them is defined as follows:

Conic set

A non-empty set S is called a cone, if:

Projection

The distance d from point \mathbf{y} \in \mathbb{R}^n to closed set S \subset \mathbb{R}^n: