A simple closure condition for the normal cone intersection formula期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

A simple closure condition for the normal cone intersection formula

Authors:	Regina Sandra Burachik Vaithilingam Jeyakumar

Affiliation:	Engenharia de Sistemas e Computacao, COPPE-UFRJ CP 68511, Rio de Janeiro-RJ, CEP 21945-970, Brazil ; Department of Applied Mathematics, University of New South Wales, Sydney 2052, Australia

Abstract:	In this paper it is shown that if and are two closed convex subsets of a Banach space and , then $N_{Ccap D}(x)=N_{C}(x)+N_{D}(x)$ 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 respectively. This closure condition is shown to be weaker than the standard interior-point-like conditions and the bounded linear regularity condition.

Keywords:	Normal cone closure condition bounded linear regularity convex optimization strong conical hull intersection property

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