Minimal Pairs of Convex Sets Which Share a Recession Cone

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