A simple closure condition for the normal cone intersection formula
Regina Sandra Burachik, V. Jeyakumar · Proceedings of the American Mathematical Society · 2004
In this paper it is shown that if C C and D D are two closed convex subsets of a Banach space X X and x ∈ C ∩ D x\in C\cap D , then N C ∩ D ( x ) = N C ( x ) + N D ( x ) N_{C\cap D}(x)=N_{C}(x)+N_{D}(x) whenever the convex cone, ( E p i σ C + E p i σ D ) \left (\mathrm {Epi} \,\sigma _{C}+\mathrm {Epi}\,\sigma _{D}\right ) , is weak* closed, where σ C \sigma _{C} and N C N_{C} are the support function and the normal cone of the set C C respectively. This closure condition is shown to be weaker than the standard interior-point-like conditions and the bounded linear regularity condition.