A Short Proof of the Sticky Face Lemma

• 成果类型: Article
• 署名作者: Robinson, Stephen M.
• 署名单位: University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-016-1037-z
• 发表日期: 2018
• 页码: 5-9
• 关键词: sets

摘要

The sticky face lemma describes the local behavior of the inverse of the normal-cone operator of a polyhedral convex set. This inverse, when applied to a vector, produces a face of the set. The lemma says that small perturbations of the vector produce only subfaces of the original face. This property is useful in analyzing variational analysis and optimization problems whose underlying sets are convex and polyhedral.