Three criteria of minimality for pairs of compact convex sets

Abstract

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 Urbański, 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).

†Dedicated to Professor D. Pallaschke on the occasion of his 65th birthday.

Keywords:

• Convex analysis
• Convex polytope
• Pairs of convex sets

Keywords:

• Mathematics Subject Classifications 2000: 52A07
• 26A27

Notes

†Dedicated to Professor D. Pallaschke on the occasion of his 65th birthday.