Three criteria of minimality for pairs of compact convex sets

摘要

In this article, we generalize the 'facets criterion' (Wiernowolski, M., 1994, A criterion for the minimality of pairs of convex compact sets. Commentationes Mathematicae, 34, 247-252) and give a new shorter proof of it (Theorem 1), formulate and prove the edges criterion (Theorem 2) and generalize the 'steps criterion' (Pallaschke, D. and Urban' ski, R., 1993, Some criteria for the minimality of pairs of compact convex sets. Methods and Models of Operations Research (ZOR), 37, 129-150) (Theorem 3).