On OM-decomposable sets

Alfredo Noel Iusem | Maxim Todorov

**Keywords:**Motzkin decomposable sets | convex sets | convex cones

We introduce and study the family of sets in a finite dimensional Enclidean space which can be written as the Minkowsky sum of an open, convex and bounded set and a closed and convex set. We establish several properties of the class of such sets, called OM-decomposable, some of which extend related properties which hold for the class of Motzkin decomposable sets (i.e., those for which the convex and bounded set in the decomposition is required to be closed, hence compact).