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Set-Valued Mappings and Enlargements of Monotone Operators
Set-valued analysis is an essential tool for the mathematical formulation of many real-life situations, e.g., equilibrium theory in mathematical economics. This work offers the first comprehensive treatment in book form of the fairly new subdiscipline of enlargements of maximal monotone operators, i...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York, NY :
Springer US : Imprint: Springer,
2008.
|
| Edición: | 1st ed. 2008. |
| Colección: | Springer Optimization and Its Applications,
8 |
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
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| 024 | 7 | |a 10.1007/978-0-387-69757-4 |2 doi | |
| 050 | 4 | |a QA319-329.9 | |
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| 100 | 1 | |a Burachik, Regina S. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Set-Valued Mappings and Enlargements of Monotone Operators |h [electronic resource] / |c by Regina S. Burachik, Alfredo N. Iusem. |
| 250 | |a 1st ed. 2008. | ||
| 264 | 1 | |a New York, NY : |b Springer US : |b Imprint: Springer, |c 2008. | |
| 300 | |a XIV, 294 p. 15 illus. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 490 | 1 | |a Springer Optimization and Its Applications, |x 1931-6836 ; |v 8 | |
| 505 | 0 | |a Set Convergence and Point-to-Set Mappings -- Convex Analysis and Fixed Point Theorems -- Maximal Monotone Operators -- Enlargements of Monotone Operators -- Recent Topics in Proximal Theory. | |
| 520 | |a Set-valued analysis is an essential tool for the mathematical formulation of many real-life situations, e.g., equilibrium theory in mathematical economics. This work offers the first comprehensive treatment in book form of the fairly new subdiscipline of enlargements of maximal monotone operators, including several important new results in the field. In the last decades, with the development of nonsmooth optimization, effective algorithms have been developed to solve these kinds of problems, such as nonsmooth variational inequalities. Several of these methods, such as bundle methods for variational problems, are fully developed and analyzed in this book. The first chapters provide a self-contained review of the basic notions and fundamental results in set-valued analysis, including set convergence and continuity of set-valued mappings together with many important results in infinite-dimensional convex analysis, leading to the classical fixed point results due to Ekeland, Caristi and Kakutani. Next, an in-depth introduction to monotone operators is developed, emphasizing results related to maximality of subdifferentials and of sums of monotone operators. Building on this foundational material, the second part of the monograph contains new results (all of them established during the last decade) on the concept of enlargements of monotone operators, with applications to variational inequalities, bundle-type methods, augmented Lagrangian methods, and proximal point algorithms. Audience This book is addressed to mathematicians, engineers, economists, and researchers interested in acquiring a solid mathematical foundation in topics such as point-to-set operators, variational inequalities, general equilibrium theory, and nonsmooth optimization, among others. Containing extensive exercises and examples throughout the text, the first four chapters of the book can also be used for a one-quarter course in set-valued analysis and maximal monotone operators for graduate students in pure and applied mathematics, mathematical economics, operations research and related areas. The only requisites, besides a minimum level of mathematical maturity, are some basic results of general topology and functional analysis. | ||
| 650 | 0 | |a Functional analysis. | |
| 650 | 0 | |a Mathematical optimization. | |
| 650 | 0 | |a Operator theory. | |
| 650 | 0 | |a Operations research. | |
| 650 | 0 | |a Management science. | |
| 650 | 0 | |a Calculus of variations. | |
| 650 | 1 | 4 | |a Functional Analysis. |
| 650 | 2 | 4 | |a Optimization. |
| 650 | 2 | 4 | |a Operator Theory. |
| 650 | 2 | 4 | |a Operations Research, Management Science . |
| 650 | 2 | 4 | |a Operations Research and Decision Theory. |
| 650 | 2 | 4 | |a Calculus of Variations and Optimization. |
| 700 | 1 | |a Iusem, Alfredo N. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 710 | 2 | |a SpringerLink (Online service) | |
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| 776 | 0 | 8 | |i Printed edition: |z 9781441943460 |
| 776 | 0 | 8 | |i Printed edition: |z 9780387517742 |
| 776 | 0 | 8 | |i Printed edition: |z 9780387697550 |
| 830 | 0 | |a Springer Optimization and Its Applications, |x 1931-6836 ; |v 8 | |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-0-387-69757-4 |z Texto Completo |
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| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||