1986/01/01 by Claude Lemaréchal, C. Lemaréchal · 1 citation
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Applied mathematics #Calculus (dental) #Computer science #Conjugacy class #Convex analysis #Convex function #Convex optimization #Differentiable function #Generalization #Geometry #Mathematical analysis #Mathematics #Optimization and Variational Analysis #Point processes and geometric inequalities #Pseudoconvex function #Pure mathematics #Regular polygon #Section (typography) #Subderivative
paper · doi:10.1080/02331938608843204
crossref issued 1986/01/01 · crossref published 1986/01/01 · crossref published-print 1986/01/01 · openalex publication_date 1986/01/01 · crossref published-online 2007/06/27 · crossref created 2007/07/08 · crossref deposited 2025/05/15 · openalex created_date 2025/10/10 · crossref indexed 2026/08/04 · openalex updated_date 2026/08/05
This is an introductory overview of nonsmooth analysis, i.e. differential study of functions which are not Frechet differentiable everywhere. In Section 1 we study how the Frechet derivative can be extended to functions which are only locally Lipschitzian. A convenient generalization is due to F, H. Clarke; we define it, give some of its properties and compare it to some other proposals. In Section 2 we study various subclasses of locally Lipschitzian functions, including semi smooth and max functions. Section 3 is exclusively devoted to convex functions, with a special study of the approximate subdifferential, illustrated by some examples (indicators, conjugacy. max functions, quadratic and piece wise linear functions). The paper deals only with that part from nonsmooth analysis that has possible applications in nonsmooth optimization. Furthermore the style is definitely intuitive and geometric.