Prove, that - is the minimum point of a convex function if and only if

Find , if

Find , if при

Find , if

Find , if

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.

What can we say about subdifferential of a convex function in those points, where the function is differentiable?

Does the subgradient coincide with the gradient of a function if the function is differentiable? Under which condition it holds?

If the function is convex on , whether always holds or not?

Find , if

Find , где , all the matrices are symmetric and defined.

Find subdifferential of a function at points and .