Motzkin predecomposable sets
The authors introduce and study a family of sets in a finite dimensional Euclidean space. Definition: A nonempty set \(F\subset\mathbb R^n\) is Motzkin predecomposable (M-predecomposable) if there exists a compact convex set \(C\) and a convex cone \(D\) such that \(F = C + D\). They show that the class of M-predecomposable sets is invariant under affine maps and Minkowski sums. They also show that faces of M-predecomposable sets are M-predecomposable as well as the existence of minimal decomposition of M-predecomposable sets. They also provide two characterizations of M-predecomposable sets both related to some properties of their faces.
scientific article; zbMATH DE number 6374615