Regularity Concepts in Nonsmooth Analysis

The results presented in this book are a product of research conducted by the author independently and in collaboration with other researchers in the field. In this light, this work encompasses the most recent collection of various concepts of regularity and nonsmooth analysis into one monograph. The first part of the book attempts to present an accessible and thorough introduction to nonsmooth analysis theory. Main concepts and some useful results are stated and illustrated through examples and exercises. The second part gathers the most prominent and recent results of various regularity concepts of sets, functions, and set-valued mappings in nonsmooth analysis. The third and final section contains six different application, with comments in relation to the existing literature.Regularity concepts have played an increasingly important role in the applications of nonsmooth analysis. The primary motivation for introducing regularity notions is to obtain equalities in calculus rules involving various constructs. This book is devoted to the study of various regularity notions in nonsmooth analysis and their applications. It is one of the first thorough studies of the regularity of functions, sets, and multifunctions, as well as their application to differential inclusions and variational inequalities. In addition to providing a thorough introduction to nonsmooth analysis, it gathers recent results of various regularity concepts of sets, functions, and set-valued mappings in nonsmooth analysis theory.