Clarke Subgradients for Directionally Lipschitzian Stratifiable Functions

• 成果类型: Article
• 署名作者: Drusvyatskiy, Dmitriy; Ioffe, Alexander D.; Lewis, Adrian S.
• 署名单位: University of Washington; University of Washington Seattle; University of Waterloo; Technion Israel Institute of Technology; Cornell University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2014.0672
• 发表日期: 2015
• 页码: 328-349
• 关键词: set-valued maps; differentiability; sard

摘要

Using a geometric argument, we show that under a reasonable continuity condition, the Clarke subdifferential of a semi-algebraic (or more generally stratifiable) directionally Lipschitzian function admits a simple form: The normal cone to the domain and limits of gradients generate the entire Clarke subdifferential. The characterization formula we obtain unifies various apparently disparate results that have appeared in the literature. Our techniques also yield a simplified proof that closed semialgebraic functions on R-n have a limiting subdifferential graph of uniform local dimension n