An Introduction to Nonsmooth Analysis.
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 de...
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Burlington :
Elsevier Science,
2013.
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| Subjects: | |
| Online Access: | CONNECT |
MARC
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| 100 | 1 | |a Ferrera, Juan. | |
| 245 | 1 | 3 | |a An Introduction to Nonsmooth Analysis. |
| 260 | |a Burlington : |b Elsevier Science, |c 2013. | ||
| 300 | |a 1 online resource (165 pages) | ||
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| 505 | 0 | |a Half Title; Title Page; Copyright; Dedication; Contents; Preface; Acknowledgment; 1 Basic Concepts and Results; 1.1 Upper and Lower Limits; 1.2 Semicontinuity; 1.3 Differentiability; 1.4 Two Important Theorems; 1.5 Problems; 2 Convex Functions; 2.1 Convex Sets and Convex Functions; 2.2 Continuity of Convex Functions; 2.3 Separation Results; 2.4 Convexity and Differentiability; 2.5 Problems; 3 The Subdifferential of a Convex Function; 3.1 Subdifferential Properties; 3.2 Two Examples; 3.3 Problems; 4 The Subdifferential: General Case; 4.1 Definition and Basic Properties. | |
| 505 | 8 | |a 4.2 Geometrical Meaning of the Subdifferential4.3 Density of Subdifferentiability Points; 4.4 Proximal Subdifferential; 4.5 Problems; 5 Calculus; 5.1 Sum Rule; 5.2 Constrained Minima; 5.3 Chain Rule; 5.4 Regular Functions: Elementary Properties; 5.5 Mean Value Results; 5.6 Decreasing Functions; 5.7 Problems; 6 Lipschitz Functions and the Generalized Gradient; 6.1 Lipschitz Regular Functions; 6.2 The Generalized Gradient; 6.3 Generalized Jacobian; 6.4 Graphical Derivative; 6.5 Problems; 7 Applications; 7.1 Flow Invariant Sets; 7.2 Viscosity Solutions; 7.3 Solving Equations; 7.4 Problems. | |
| 505 | 8 | |a BibliographyIndex. | |
| 520 | |a 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 gradientsIncludes also the main tools of the theory, as Sum and Chain Rules or Mean Value theoremsContent is introduced in an elementary way, developing many examples, allowing the reader to understand a theory which. | ||
| 504 | |a Includes bibliographical references and index. | ||
| 500 | |a ScienceDirect eBook - Mathematics 2013 |5 TMurS | ||
| 650 | 0 | |a Nonsmooth optimization. | |
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| 776 | 0 | 8 | |i Print version: |a Ferrera, Juan. |t An Introduction to Nonsmooth Analysis. |d Burlington : Elsevier Science, ©2013 |z 9780128007310 |
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