Set-Valued and Variational Analysis

, Volume 21, Issue 4, pp 635–647 | Cite as

On the Stability of the Motzkin Representation of Closed Convex Sets

  • M. A. Goberna
  • M. I. TodorovEmail author


A set is called Motzkin decomposable when it can be expressed as the Minkowski sum of a compact convex set with a closed convex cone. This paper analyzes the continuity properties of the set-valued mapping associating to each couple \(\left( C,D\right) \) formed by a compact convex set C and a closed convex cone D its Minkowski sum C + D. The continuity properties of other related mappings are also analyzed.


Motzkin decomposition Minkowski sum Stability 


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© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Statistics and Operations ResearchUniversidad de AlicanteAlicanteSpain
  2. 2.Department Actuary and MathematicsUniversidad de las AméricasCholulaMexico

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