Convex Analysis and Optimization in Hadamard Spaces
Seiten
2014
De Gruyter (Verlag)
978-3-11-036103-2 (ISBN)
De Gruyter (Verlag)
978-3-11-036103-2 (ISBN)
The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Please submit book proposals to Jürgen Appell.
In the past two decades, convex analysis and optimization have been developed in Hadamard spaces. This book represents a first attempt to give a systematic account on the subject. Hadamard spaces are complete geodesic spaces of nonpositive curvature. They include Hilbert spaces, Hadamard manifolds, Euclidean buildings and many other important spaces. While the role of Hadamard spaces in geometry and geometric group theory has been studied for a long time, first analytical results appeared as late as in the 1990s. Remarkably, it turns out that Hadamard spaces are appropriate for the theory of convex sets and convex functions outside of linear spaces. Since convexity underpins a large number of results in the geometry of Hadamard spaces, we believe that its systematic study is of substantial interest. Optimization methods then address various computational issues and provide us with approximation algorithms which may be useful in sciences and engineering. We present a detailed description of such an application to computational phylogenetics. The book is primarily aimed at both graduate students and researchers in analysis and optimization, but it is accessible to advanced undergraduate students as well.
In the past two decades, convex analysis and optimization have been developed in Hadamard spaces. This book represents a first attempt to give a systematic account on the subject. Hadamard spaces are complete geodesic spaces of nonpositive curvature. They include Hilbert spaces, Hadamard manifolds, Euclidean buildings and many other important spaces. While the role of Hadamard spaces in geometry and geometric group theory has been studied for a long time, first analytical results appeared as late as in the 1990s. Remarkably, it turns out that Hadamard spaces are appropriate for the theory of convex sets and convex functions outside of linear spaces. Since convexity underpins a large number of results in the geometry of Hadamard spaces, we believe that its systematic study is of substantial interest. Optimization methods then address various computational issues and provide us with approximation algorithms which may be useful in sciences and engineering. We present a detailed description of such an application to computational phylogenetics. The book is primarily aimed at both graduate students and researchers in analysis and optimization, but it is accessible to advanced undergraduate students as well.
Miroslav Bačák, MPI Leipzig, Germany.
"[...] very well-written and readable book [...].The careful and detailed discussions of both theory and applications render this interesting and timely book accessible to researchers and students alike." Mathematical Reviews
| Erscheint lt. Verlag | 29.9.2014 |
|---|---|
| Reihe/Serie | De Gruyter Series in Nonlinear Analysis and Applications ; 22 |
| Verlagsort | Berlin/Boston |
| Sprache | englisch |
| Maße | 170 x 240 mm |
| Gewicht | 472 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| Schlagworte | Convex Analysis • Convex analysis; Convex optimization; Hadamard space; Metric geometry; Nonpositive curvature; Geodesic convexity • Convex Optimization • Geodesic convexity • Hadamardräume • Hadamard space • Konvexe Analysis • Konvexe Optimierung • metric geometry • Nonpositive curvature |
| ISBN-10 | 3-11-036103-5 / 3110361035 |
| ISBN-13 | 978-3-11-036103-2 / 9783110361032 |
| Zustand | Neuware |
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