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Convex analysis in general vector spaces /
Annotation The primary aim of this book is to present the conjugate and sub/differential calculus using the method of perturbation functions in order to obtain the most general results in this field. The secondary aim is to provide important applications of this calculus and of the properties of con...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
River Edge, N.J. ; London :
World Scientific,
©2002.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Zalinescu, C., |d 1952- | |
| 245 | 1 | 0 | |a Convex analysis in general vector spaces / |c C Zălinescu. |
| 260 | |a River Edge, N.J. ; |a London : |b World Scientific, |c ©2002. | ||
| 300 | |a 1 online resource (xx, 367 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 504 | |a Includes bibliographical references (pages 349-357) and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | 8 | |a Annotation The primary aim of this book is to present the conjugate and sub/differential calculus using the method of perturbation functions in order to obtain the most general results in this field. The secondary aim is to provide important applications of this calculus and of the properties of convex functions. Such applications are: the study of well-conditioned convex functions, uniformly convex and uniformly smooth convex functions, best approximation problems, characterizations of convexity, the study of the sets of weak sharp minima, well-behaved functions and the existence of global error bounds for convex inequalities, as well as the study of monotone multifunctions by using convex functions. | |
| 505 | 0 | |a Ch. 1. Preliminary results on functional analysis. 1.1. Preliminary notions and results. 1.2. Closedness and interiority notions. 1.3. Open mapping theorems. 1.4. Variational principles. 1.5. Exercises. 1.6. Bibliographical notes -- ch. 2. Convex analysis in locally convex spaces. 2.1. Convex functions. 2.2. Semi-continuity of convex functions. 2.3. Conjugate functions. 2.4. The subdifferential of a convex function. 2.5. The general problem of convex programming. 2.6. Perturbed problems. 2.7. The fundamental duality formula. 2.8. Formulas for conjugates and e-subdifferentials, duality relations and optimality conditions. 2.9. Convex optimization with constraints. 2.10. A minimax theorem. 2.11. Exercises. 2.12. Bibliographical notes -- ch. 3. Some results and applications of convex analysis in normed spaces. 3.1. Further fundamental results in convex analysis. 3.2. Convexity and monotonicity of subdifferentials. 3.3. Some classes of functions of a real variable and differentiability of convex functions. 3.4. Well conditioned functions. 3.5. Uniformly convex and uniformly smooth convex functions. 3.6. Uniformly convex and uniformly smooth convex functions on bounded sets. 3.7. Applications to the geometry of normed spaces. 3.8. Applications to the best approximation problem. 3.9. Characterizations of convexity in terms of smoothness. 3.10. Weak sharp minima, well-behaved functions and global error bounds for convex inequalities. 3.11. Monotone multifunctions. 3.12. Exercises. 3.13. Bibliographical notes. | |
| 546 | |a English. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Convex functions. | |
| 650 | 0 | |a Convex sets. | |
| 650 | 0 | |a Functional analysis. | |
| 650 | 0 | |a Vector spaces. | |
| 650 | 6 | |a Fonctions convexes. | |
| 650 | 6 | |a Ensembles convexes. | |
| 650 | 6 | |a Analyse fonctionnelle. | |
| 650 | 6 | |a Espaces vectoriels. | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a Convex functions |2 fast | |
| 650 | 7 | |a Convex sets |2 fast | |
| 650 | 7 | |a Functional analysis |2 fast | |
| 650 | 7 | |a Vector spaces |2 fast | |
| 776 | 0 | 8 | |i Print version: |a Zalinescu, C., 1952- |t Convex analysis in general vector spaces. |d River Edge, NJ : World Scientific, ©2002 |z 9812380671 |z 9789812380678 |w (DLC) 2002069000 |w (OCoLC)49959262 |
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