A simple closure condition for the normal cone intersection formula

Burachik, Regina; Jeyakumar, Vaithilingam

doi:10.1090/S0002-9939-04-07844-X

A simple closure condition for the normal cone intersection formula
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by Regina Sandra Burachik and Vaithilingam Jeyakumar PDF

Proc. Amer. Math. Soc. 133 (2005), 1741-1748 Request permission

Abstract:

In this paper it is shown that if $C$ and $D$ are two closed convex subsets of a Banach space $X$ and $x\in C\cap D$, then $N_{C\cap D}(x)=N_{C}(x)+N_{D}(x)$ whenever the convex cone, $\left (\mathrm {Epi} \sigma _{C}+\mathrm {Epi} \sigma _{D}\right )$, is weak* closed, where $\sigma _{C}$ and $N_{C}$ are the support function and the normal cone of the set $C$ respectively. This closure condition is shown to be weaker than the standard interior-point-like conditions and the bounded linear regularity condition.

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