02-02 Some important examples

이 절에서는 convex set의 주요 예제들을 살펴본다.

  • Trivial ones: empty set, point, line, line segment, ray
  • Hyperplane: {x:aTx=b}, for given a,b, a0
  • Halfspace: {x:aTx}b for a0
  • Affine space: {x:Ax=b}, for given A,b
  • Euclidean ball & ellipsoid
  • Norm ball: {x:xr}, for given norm · , radius r
  • Convex cone : norm cone, normal cone, positive semidefinite cone