  Robinson introduced a quotient space of pairs of convex sets which share
their recession cone. In this paper minimal pairs of unbounded convex sets,
i.e. minimal representations of elements of Robinson's spaces are investigated.
The fact that a minimal pair having property of translation is reduced is
proved. In the case of pairs of two-dimensional sets a formula for an
equivalent minimal pair is given, a criterion of minimality of a pair of sets
is presented and reducibility of all minimal pairs is proved.
Shephard--Weil--Schneider's criterion for polytopal summand of a compact convex
set is generalized to unbounded convex sets. An application of minimal pairs of
unbounded convex sets to Hartman's minimal representation of dc-functions is
shown. Examples of minimal pairs of three-dimensional sets are given.
