# Regularity Concepts in Nonsmooth Analysis

## Theory and Applications

• MessaoudÂ Bounkhel
Book

Part of the Springer Optimization and Its Applications book series (SOIA, volume 59)

1. Front Matter
Pages i-xv
2. ### Nonsmooth Analysis Theory

1. Front Matter
Pages 1-1
2. Messaoud Bounkhel
Pages 3-30
3. ### Regularity Concepts in Nonsmooth Analysis Theory

1. Front Matter
Pages 31-31
2. Messaoud Bounkhel
Pages 33-71
3. Messaoud Bounkhel
Pages 73-85
4. Messaoud Bounkhel
Pages 87-124
4. ### Applications of Nonsmooth Analysis Theory

1. Front Matter
Pages 125-125
2. Messaoud Bounkhel
Pages 127-164
3. Messaoud Bounkhel
Pages 165-209
4. Messaoud Bounkhel
Pages 211-225
5. Messaoud Bounkhel
Pages 227-246
5. Back Matter
Pages 247-261

### Introduction

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.

Regularity Concepts in Nonsmooth Analysis is divided into three accessible parts. The first section presents a thorough introduction to nonsmooth analysis theory, using examples and exercises to explain main concepts and show useful results. The second part demonstrates the most recent results of various regularity concepts of sets, functions, and set-valued mappings in nonsmooth analysis. The final section addresses different applications, including first order and second order differential inclusions, quasi-variational, and equilibrium theory.

This book is designed for graduate students, researchers, and general practitioners interested in the applications of nonsmooth analysis.

### Keywords

Differential Inclusions Equilibrium Problems Nonsmooth Analysis Regularity concepts Variational Inequalities

#### Authors and affiliations

• MessaoudÂ Bounkhel
• 1
1. 1.College of Science, Department of MathematicsKing Saud UniversityRiyadhSaudi Arabia

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4614-1019-5