  A closed convex subset of a normed linear space is said to have the strong
separation property if it can be strongly separated from every other disjoint
closed and convex set by a closed hyperplane. In this paper we give some
results on the separation of convex sets with noticing the role of barrier
cones, develop some characterizations of subsets having the strong separation
property, and apply them to consider a class of convex optimization problems.
