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