Convex Analysis and Optimization in Hadamard Spaces

Miroslav Bacak

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English

De Gruyter
29 September 2014

Calculus & mathematical analysis; Functional analysis & transforms; Calculus of variations; Optimisation; Combinatorics & graph theory

Series: De Gruyter Series in Nonlinear Analysis & Applications

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.

By: Miroslav Bacak
Imprint: De Gruyter
Country of Publication: Germany
Edition: Digital original
Volume: 22
Dimensions: Height: 240mm, Width: 170mm,
Weight: 458g
ISBN: 9783110361032
ISBN 10: 3110361035
Series: De Gruyter Series in Nonlinear Analysis & Applications
Pages: 193
Publication Date: 29 September 2014
Recommended Age: College Graduate Student
Audience: Professional and scholarly , Undergraduate , Undergraduate
Format: Hardback
Publisher's Status: Active

Miroslav Ba?ak, MPI Leipzig, Germany.

Reviews for Convex Analysis and Optimization in Hadamard Spaces

[...] 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