02-02 Some important examples

이 절에서는 convex set의 주요 예제들을 살펴본다.

• Trivial ones: empty set, point, line, line segment, ray
• Hyperplane: $\{x:a^{T}x=b\}$, for given $a,b$, $a\ne 0$
• Halfspace: $\{x:a^{T}x\le \}b$ for $a\ne 0$
• Affine space: $\{x:Ax=b\}$, for given $A,b$
• Euclidean ball & ellipsoid
• Norm ball: $\{x:\Vert x\Vert \le r\}$, for given norm $\Vert ·\Vert$ , radius r
• Convex cone : norm cone, normal cone, positive semidefinite cone