  Exhausters and coexhausters are notions of constructive nonsmooth analysis
which are used to study extremal properties of functions. An upper exhauster
(coexhauster) is used to get an approximation of a considered function in the
neighborhood of a point in the form of $\min\max$ of linear (affine) functions.
A lower exhauster (coexhauster) is used to represent the approximation in the
form of $\max\min$ of linear (affine) functions. Conditions for a minimum in a
most simple way are expressed by means of upper exhausters and coexhausters,
while conditions for a maximum are described in terms of lower exhausters and
coexhausters. Thus the problem of obtaining an upper exhauster or coexhauster
when the lower one is given and vice verse arises. We study this problem in the
paper and propose new method for its solution which allows one to pass easily
between $\min\max$ and $\max\min$ representations.
