Closed convex sets of Motzkin and generalized Minkowski types

TL;DR

This paper characterizes generalized Minkowski sets and Motzkin decomposable sets, focusing on closed convex sets with unique minimal faces and their epigraphic forms, advancing understanding of their structure.

Contribution

It introduces new characterizations of generalized Minkowski sets and Motzkin decomposable sets, especially those with a single minimal face, including their epigraphic versions.

Findings

Characterization of generalized Minkowski sets

New insights into Motzkin decomposable sets

Analysis of closed convex sets with a single minimal face

Abstract

The aim of this paper is twofold. On one hand the generalized Minkowski sets are defined and characterized. On the other hand, the Motzkin decomposable sets, along with their epigraphic versions are considered and characterized in new ways. Among them, the closed convex sets with one single minimal face, i.e. translated closed convex cones, along with their epigraphic counterparts are particularly studied.