Abstract
Robinson introduced a quotient space of pairs of unbounded 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 quotient spaces, are investigated. The fact that a minimal pair having a property of translation is reduced is proved. In the case of pairs of two-dimensional sets a formula for finding an equivalent minimal pair is given, a criterion of minimality of a pair of sets is presented, reducibility of all minimal pairs is proved, and nontrivial examples are shown. Shephard--Weil--Schneider's criterion for polytopal summand of a compact convex set is generalized to unbounded convex sets. Finally, minimal pairs of unbounded convex sets are applied to finding Hartman's minimal representation of differences of convex functions.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
