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An Introduction to Nonsmooth Analysis Juan Ferrera (Universidad Complutense de Madrid, Spain)

An Introduction to Nonsmooth Analysis By Juan Ferrera (Universidad Complutense de Madrid, Spain)

An Introduction to Nonsmooth Analysis by Juan Ferrera (Universidad Complutense de Madrid, Spain)

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Summary

A handbook for undergraduate and graduate students of mathematics that introduce nonsmooth analysis. It includes different kinds of sub and super differentials as well as generalized gradients. It also presents the main tools of the theory, as Sum and Chain Rules or Mean Value theorems.

An Introduction to Nonsmooth Analysis Summary

An Introduction to Nonsmooth Analysis by Juan Ferrera (Universidad Complutense de Madrid, Spain)

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.

An Introduction to Nonsmooth Analysis Reviews

...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

Table of Contents

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.

Additional information

NLS9780128007310
9780128007310
0128007311
An Introduction to Nonsmooth Analysis by Juan Ferrera (Universidad Complutense de Madrid, Spain)
Juan Ferrera (Universidad Complutense de Madrid, Spain)
New
Paperback
Elsevier Science Publishing Co Inc
2013-11-26
164
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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