Bounded linear regularity of convex sets in Banach spaces and its applications

• 成果类型: Article
• 署名作者: Song, W; Zang, R
• 署名单位: Harbin Normal University; Chinese University of Hong Kong
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-005-0596-1
• 发表日期: 2006
• 页码: 59-79
• 关键词: constraint qualifications; error-bounds; Duality; intersection

摘要

This paper deals with bounded linear regularity, linear regularity and the strong conical hull intersection property (CHIP) of a collection of finitely many closed convex intersecting sets in Banach spaces. It is shown that, as in finite dimensional space setting (see [6]), the standard constraint qualification implies bounded linear regularity, which in turn yields the strong conical hull intersection property, and that the collection of closed convex sets {C-1, . . . ,C-n} is bounded linearly regular if and only if the tangent cones of {C-1, . . . ,C-n} has the CHIP and the normal cones of {C-1, . . . ,C-n} has the property (G)(uniformly on a neighborhood in the intersection C). As applications, we study the global error bounds for systems of linear and convex inequalities.