Characteristic properties of primal exhausters for various classes of positively homogeneous functions

The paper deals with the exhaustive families of upper convex approximations (the primal upper exhausters) and the exhaustive families of lower concave approximations (the primal lower exhausters) of positively homogeneous functions defined on finite dimensional vector spaces. We give a comprehensive description of characteristic properties of the primal upper and lower exhausters for Lipshitzian positively homogeneous functions as well as for difference-sublinear and piecewise linear functions.