2012/11/15 by Dmitriy Drusvyatskiy, Drusvyatskiy, Dmitriy, A. D. Ioffe +3
Computer Science · Engineering · Mathematics · #49J53 #65K10 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Primary: 49J52 #Secondary: 90C46
paper · pdf · doi:10.48550/arxiv.1211.3615
openalex publication_date 2012/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using a geometric argument, we show that under a reasonable continuity\ncondition, the Clarke subdifferential of a semi-algebraic (or more generally\nstratifiable) directionally Lipschitzian function admits a simple form: the\nnormal cone to the domain and limits of gradients generate the entire Clarke\nsubdifferential. The characterization formula we obtain unifies various\napparently disparate results that have appeared in the literature. Our\ntechniques also yield a simplified proof that closed semialgebraic functions on\n Rn have a limiting subdifferential graph of uniform local dimension n.\n