Motzkin predecomposable sets

We introduce and study the family of sets in a finite dimensional Euclidean space which can be written as the Minkowski sum of a compact and convex set and a convex cone (not necessarily closed). We establish several properties of the class of such sets, called Motzkin predecomposable, some of which hold also for the class of Motzkin decomposable sets (i.e., those for which the convex cone in the decomposition is requested to be closed), while others are specific of the new family

Weakly Motzkin Predecomposable Sets

J. E. Martínez-Legaz was partially supported by the MINECO of Spain, Grant MTM2014-59179-C2-2-P, the Severo Ochoa Programme for Centres of Excellence in R&D [SEV-2015-0563], and under the Australian Research Council's Discovery Projects funding scheme (project number DP140103213). He is affiliated with MOVE (Markets, Organizations and Votes in Economics). M. I. Todorov was partially supported by the MINECO of Spain and ERDF of EU, Grant MTM2014-59179-C2-1-P, and Sistema Nacional de Investigadores, Mexico.Altres ajuts: Australian Research Council DP140103213We introduce and study the class of weakly Motzkin predecomposable sets, which are those sets in ℝ n that can be expressed as the Minkowski sum of a bounded convex set and a convex cone, none of them being necessarily closed. This class contains that of Motzkin predecomposable sets, for which the bounded components are compact, which in turn contains the class of Motzkin decomposable sets, for which the bounded components are compact and the conic components are closed

A subdifferential characterization of Motzkin decomposable functions

The paper provides a new subdifferential characterization for Motzkin decomposable (convex) functions. This characterization leads to diverse stability properties for such a decomposability for operations like addition and composition

Weakly Motzkin Predecomposable Sets

J. E. Martínez-Legaz was partially supported by the MINECO of Spain, Grant MTM2014-59179-C2-2-P, the Severo Ochoa Programme for Centres of Excellence in R&D [SEV-2015-0563], and under the Australian Research Council's Discovery Projects funding scheme (project number DP140103213). He is affiliated with MOVE (Markets, Organizations and Votes in Economics). M. I. Todorov was partially supported by the MINECO of Spain and ERDF of EU, Grant MTM2014-59179-C2-1-P, and Sistema Nacional de Investigadores, Mexico.We introduce and study the class of weakly Motzkin predecomposable sets, which are those sets in ℝ n that can be expressed as the Minkowski sum of a bounded convex set and a convex cone, none of them being necessarily closed. This class contains that of Motzkin predecomposable sets, for which the bounded components are compact, which in turn contains the class of Motzkin decomposable sets, for which the bounded components are compact and the conic components are closed