02 - Must-learn optimization concepts - Hyperplanes and halfspaces

In this video we will learn three different ways of understanding of a hyperplanes. The first way of understanding is analytical and the two other ones are geometrical. We will see a hyperplane is the solution set of a linear equation. Geometrically, it can be interpreted as an offset, plus all vectors orthogonal to the normal vector. We also learn that hyperplanes are affine sets. Once you learn the concept of a hyperplane you can easily understand a halfspace. Halfspaces are not affine sets but they are convex sets. Link to exercise 2.5 about hyperplanes:    • Convex optimization book - solution - exer...   Links to exercise 2.5, 2.6, and 2.7 about halfspaces:    • Convex optimization book - solution - exer...      • Convex optimization book - solution - exer...      • Convex optimization book - solution - exer...