Regularity Concepts in Nonsmooth Analysis Theory and Applications [Paperback]

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.

1. Nonsmooth Concepts.- 2. Regularity.- 3. Regularity of Functions.- 4. Regularity of Set-Valued Mappings.- 5. First Order Differential Inclusions.- 6. Second Order Differential Inclusions.- 7. Quasi-Variational Inequalities.- 8. Time Dependent Quasi-Variational Inequalities.- 9. Economic Problems and Equilibrium Theory.- Index.

Regularity concepts have played an increasingly important role in the applications of nonsmooth analysis, including differential inclusions, optimization, and variational inequalities. This heightened role has made it beneficial to introduce graduate students and young researchers to the basic concepts of regularity and their applications. This book is devoted to the study of various regularity notions in nonsmooth analysis and their applications. It is the first thorough study of the regularity of functions, sets, and multifunctions, as well as their applications to differential inclusions and variational inequalities.

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Regularity Concepts in Nonsmooth Analysis is divided into three accessible parts. The first section presents a thorough introduction to nonsmooth anal“\