Generalized Differentiation with Positively Homogeneous Maps: Applications in Set-Valued Analysis and Metric Regularity

• 成果类型: Article
• 署名作者: Pang, C. H. Jeffrey
• 署名单位: Massachusetts Institute of Technology (MIT)
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1110.0497
• 发表日期: 2011
• 页码: 377-397
• 关键词: calculus; mappings; MULTIFUNCTIONS; optimization; nonsmooth; openness

摘要

We propose a new concept of generalized differentiation of set-valued maps that captures first-order information. This concept encompasses the standard notions of Frechet differentiability, strict differentiability, calmness and Lipschitz continuity in single-valued maps, and the Aubin property and Lipschitz continuity in set-valued maps. We present calculus rules, sharpen the relationship between the Aubin property and coderivatives, and study how metric regularity and open covering can be refined to have a directional property similar to our concept of generalized differentiation. Finally, we discuss the relationship between the robust form of generalized differentiation and its one-sided counterpart.