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: \(\{x : \| x \| ≤ r\}\), for given norm \(\|·\|\) , radius r
• Convex cone : norm cone, normal cone, positive semidefinite cone