Preprint A699/2011
Motzkin decomposition of closed convex sets via truncation

Maxim Todorov | Goberna, Miguel | Iusem, Alfredo | Martinez-Legaz, Juan Enrique

**Keywords: **
Motzkin decomposition | closed convex sets | convex functions

A nonempty set F is called Motzkin decomposable when it can be expressed as the Minkowski sum of a compact convex set C and a closed convex cone D. C and D are called compact and conic components of F. This paper provides a new characterization of the Motzkin decomposable sets involving truncations (i.e., intersections of halfspaces with F, when F contains no lines. and with the orthogonal complement of the affine hull of
F otherwise).