TY - JOUR
T1 - Weakly Motzkin Predecomposable Sets
AU - Martínez-Legaz, J. E.
AU - Todorov, M. I.
PY - 2017/9/1
Y1 - 2017/9/1
N2 - © 2017, Springer Science+Business Media Dordrecht. 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.
AB - © 2017, Springer Science+Business Media Dordrecht. 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.
KW - Convex cones
KW - Convex sets
KW - Motzkin decomposable sets
U2 - 10.1007/s11228-017-0420-0
DO - 10.1007/s11228-017-0420-0
M3 - Article
SN - 1877-0533
VL - 25
SP - 507
EP - 516
JO - Set-Valued and Variational Analysis
JF - Set-Valued and Variational Analysis
IS - 3
ER -