Techniques for Nonsmooth Analysis on Smooth Manifolds II: Deformations and Flows

摘要

Nonsmooth analysis, differential analysis for functions without differentiability, has witnessed a rapid growth in the past several decades stimulated by intrinsic nonsmooth phenomena in control theory, optimization, mathematical economics and many other fields. In the past several years many problems in control theory, matrix analysis and geometry naturally led to an increasing interest in nondifferentiable functions on smooth manifolds. Since a smooth manifold is only locally resembles a Euclidean space and, in general, lacks of a linear structure, new techniques are needed for adequately address these problems. A number of results and techniques for dealing with such problems have emerged recently [6, 13, 15, 25].