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An Introduction to Nonsmooth Analysis de Juan Ferrera

An Introduction to Nonsmooth Analysis

Autor Juan Ferrera
en Limba Engleză Paperback – 25 noi 2013
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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Specificații

ISBN-13: 9780128007310
ISBN-10: 0128007311
Pagini: 164
Ilustrații: black & white illustrations
Dimensiuni: 152 x 229 x 9 mm
Greutate: 0.23 kg
Ediția:New.
Editura: ELSEVIER SCIENCE

Public țintă

This book is mainly directed to graduate students in mathematics. It may be used as handbook for a graduate course or a reference book in an undergraduate course of advanced analysis with the aim of introduce the nonsmooth analysis as a complement to differential calculus, showing how smooth tools can be employed in the lack of differentiability.

Cuprins

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

Recenzii

"...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
"...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