An Introduction to Nonsmooth Analysis

An Introduction to Nonsmooth Analysis

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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.
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Product details

  • Paperback | 164 pages
  • 149.86 x 226.06 x 10.16mm | 249.47g
  • Academic Press Inc
  • San Diego, United States
  • English
  • black & white illustrations
  • 0128007311
  • 9780128007310
  • 1,771,648

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.
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Review quote

"...starting from the very beginning, adopting a slow, easy to follow linear development and reaching to a self-contained theory...oriented towards undergraduate students, as a first quick introduction to the topic."--MathSciNet, An Introduction to Nonsmooth Analysis

"...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
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