Convex analysis and optimization in Hadamard spaces / Miroslav Bacak.

Format:

Book

Author/Creator:

Bacak, Miroslav, author.

Series:

De Gruyter series in nonlinear analysis and applications ; Volume 22.

De Gruyter Series in Nonlinear Analysis and Applications, 0941-813x ; Volume 22

Language:

English

Subjects (All):

Metric spaces.

G-spaces.

Hadamard matrices.

Physical Description:

1 online resource (194 p.)

Edition:

1st ed.

Place of Publication:

Berlin, [Germany] ; Boston, [Massachusetts] : Walter de Gruyter GmbH, 2014.

Language Note:

English

Summary:

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 1990's. 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.

Contents:

Front matter

Preface

Contents

1 Geometry of Nonpositive Curvature

2 Convex sets and convex functions

3 Weak convergence in Hadamard spaces

4 Nonexpansive mappings

5 Gradient flow of a convex functional

6 Convex optimization algorithms

7 Probabilistic tools in Hadamard spaces

8 Tree space and its applications

References

Index

Back matter

Notes:

Description based upon print version of record.

Description based on print version record.

Includes bibliographical references and index.

ISBN:

9783110361629

3110361620

9783110391084

3110391082

OCLC:

1023977505