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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...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Burlington :
Elsevier Science,
2013.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.
- 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.
- BibliographyIndex.