Buch, Englisch, 294 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 476 g
Buch, Englisch, 294 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 476 g
Reihe: Springer Optimization and Its Applications
ISBN: 978-1-4419-4346-0
Verlag: Springer US
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.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
- Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik
- Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe
- Mathematik | Informatik Mathematik Operations Research Spieltheorie
- Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Ökonometrie
- Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
- Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
Weitere Infos & Material
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.
