Subgradient and subdifferential

  1. Prove, that - is the minimum point of a convex function if and only if
  2. Find , if
  3. Find , if при
  4. Find , if
  5. Find , if
  6. Describe the connection between subgradient of a scalar function and global linear lower bound, which support (tangent) the graph of the function at a point.
  7. What can we say about subdifferential of a convex function in those points, where the function is differentiable?
  8. Does the subgradient coincide with the gradient of a function if the function is differentiable? Under which condition it holds?
  9. If the function is convex on , whether always holds or not?
  10. Find , if
  11. Find , где , all the matrices are symmetric and defined.
  12. Find subdifferential of a function at points and .