An Introduction To Nonsmooth Analysis by Juan Ferrera

An Introduction To Nonsmooth Analysis

byJuan FerreraEditorJuan Ferrera

Paperback | November 26, 2013

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Nonsmooth Analysis is a relatively recent area of mathematical analysis. The literature about this subject consists mainly in research papers and books. The purpose of this book is to provide a handbook for undergraduate and graduate students of mathematics that introduce this interesting area in detail.

  • Includes different kinds of sub and super differentials as well as generalized gradients
  • Includes also the main tools of the theory, as Sum and Chain Rules or Mean Value theorems
  • Content is introduced in an elementary way, developing many examples, allowing the reader to understand a theory which is scattered in many papers and research books

Details & Specs

Title:An Introduction To Nonsmooth AnalysisFormat:PaperbackDimensions:164 pages, 8.75 × 6.35 × 0.68 inPublished:November 26, 2013Publisher:Academic PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0128007311

ISBN - 13:9780128007310

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Table of Contents

Chapter 1. Basic concepts and results: Upper and lower limits. Semicontinuity. Differentiability. Two important Theorems.
Chapter 2. Convex Functions: Convex sets and convex functions. Continuity of convex functions. Separation Results. Convexity and Differentiability.
Chapter 3. The subdifferential of a Convex function: Subdifferential properties. Examples.
Chapter 4. The subdifferential. General case: Definition and basic properties. Geometrical meaning of the subdifferential. Density of subdifferentiability points. Proximal subdifferential
Chapter 5. Calculus: Sum Rule. Constrained minima. Chain Rule. Regular functions: Elementary properties. Mean Value results. Decreasing Functions
Chapter 6. Lipschitz functions and the generalized gradient: Lipschitz regular functions. The generalized gradient. Generalized Jacobian. Graphical derivative
Chapter 7. Applications: Flow invariant sets. Viscosity solutions. Solving equations.

Editorial Reviews

"...devoted to presenting the theory of the subdifferential of lower semicontinuous functions which is a generalization of the subdifferential of convex functions...a good reference for researchers in optimization and applied mathematics."--Zentralblatt MATH, Sep-14