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An Introduction to Nonsmooth Analysis

  • ID: 2719459
  • Book
  • November 2013
  • 164 Pages
  • Elsevier Science and Technology
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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

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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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Ferrera, Juan
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