Separation

  1. Let are closed convex sets such that: . Is it true that
  2. Find a separating hyperplane between and :

  3. Find a supporting hyperplane for a set of at the boundary point
  4. Find a supporting hyperplane for the set of such that separates it from the point
  5. Приведите пример двух строго, но не сильно отделимых множеств. Двух отделимых, но не собственно отделимых множеств.
  6. Illustrate the difference between the tangenti hyperplane and the separating hyperplane by considering a convex set with a non-smooth boundary.
  7. Derive the equation of the supporting hyperplane of the set of at (any choice)
  8. Derive the equation of the supporting hyperplane of the set of , which separates it from the points (any choice)
  9. Find a separating hyperplane between and :

  10. Find a supporting hyperplane for a set at the border point