Regularity conditions for
the linear separation of sets
Giancarlo Bigi and Massimo Pappalardo
In recent papers, a concept of regularity for linear separation
between a set K and a convex cone
H has been introduced and
characterized. Regular separation does not prevent the existence
of an irregular one; thus, a concept of total regularity, ensuring
that only regular separation holds, has been here investigated.
We point out that regularity and total regularity conditions
strengthen the concept of proper separation.
In the same papers, constrained extremum problems have been analysed
within this framework through generalized systems and image space
approach; this kind of analysis has led to constraint qualifications
and regularity conditions for Karush-Kuhn-Tucker multipliers,
which generalize well known ones.
In this paper we extend the analysis of linear separation to a more
general setting. We want to deepen the study of proper separation,
concentrating our attention to the inclusion of a generic face of the
cone H into separating hyperplanes.
In particular, we are interested in
conditions which ensure that the given face is not included in at
least one or in every separating hyperplane. To this aim we introduce
the concepts of regularity and total regularity with respect to a face
and we characterize them.
If you are interested in this paper, feel free to contact me.
My Home Page