# Riemannian Optimization and Its Applications

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- Author : Hiroyuki Sato
- Publisher : Springer Nature
- Release : 17 February 2021
- ISBN : 9783030623913
- Page : 129 pages
- Rating : 4.5/5 from 103 voters

## Download Riemannian Optimization and Its Applications in PDF, Epub and Kindle

This brief describes the basics of Riemannian optimization—optimization on Riemannian manifolds—introduces algorithms for Riemannian optimization problems, discusses the theoretical properties of these algorithms, and suggests possible applications of Riemannian optimization to problems in other fields. To provide the reader with a smooth introduction to Riemannian optimization, brief reviews of mathematical optimization in Euclidean spaces and Riemannian geometry are included. Riemannian optimization is then introduced by merging these concepts. In particular, the Euclidean and Riemannian conjugate gradient methods are discussed in detail. A brief review of recent developments in Riemannian optimization is also provided. Riemannian optimization methods are applicable to many problems in various fields. This brief discusses some important applications including the eigenvalue and singular value decompositions in numerical linear algebra, optimal model reduction in control engineering, and canonical correlation analysis in statistics.

### Riemannian Optimization and Its Applications

- Author : Hiroyuki Sato
- Publisher : Springer Nature
- Release Date : 2021-02-17
- ISBN : 9783030623913

This brief describes the basics of Riemannian optimization—optimization on Riemannian manifolds—introduces algorithms for Riemannian optimization problems, discusses the theoretical properties of these algorithms, and suggests possible applications of Riemannian optimization to problems in other fields. To provide the reader with a smooth introduction to Riemannian optimization, brief reviews of mathematical optimization in Euclidean spaces and Riemannian geometry are included. Riemannian optimization is then introduced by merging these concepts. In particular, the Euclidean and Riemannian conjugate gradient methods are

### Convex Functions and Optimization Methods on Riemannian Manifolds

- Author : C. Udriste
- Publisher : Springer Science & Business Media
- Release Date : 2013-11-11
- ISBN : 9789401583909

The object of this book is to present the basic facts of convex functions, standard dynamical systems, descent numerical algorithms and some computer programs on Riemannian manifolds in a form suitable for applied mathematicians, scientists and engineers. It contains mathematical information on these subjects and applications distributed in seven chapters whose topics are close to my own areas of research: Metric properties of Riemannian manifolds, First and second variations of the p-energy of a curve; Convex functions on Riemannian manifolds;

### Nonsmooth Optimization and Its Applications

- Author : Seyedehsomayeh Hosseini,Boris S. Mordukhovich,André Uschmajew
- Publisher : Springer
- Release Date : 2019-03-29
- ISBN : 9783030113704

Since nonsmooth optimization problems arise in a diverse range of real-world applications, the potential impact of efficient methods for solving such problems is undeniable. Even solving difficult smooth problems sometimes requires the use of nonsmooth optimization methods, in order to either reduce the problem’s scale or simplify its structure. Accordingly, the field of nonsmooth optimization is an important area of mathematical programming that is based on by now classical concepts of variational analysis and generalized derivatives, and has developed

### Algorithmic Advances in Riemannian Geometry and Applications

- Author : Hà Quang Minh,Vittorio Murino
- Publisher : Springer
- Release Date : 2016-10-05
- ISBN : 9783319450261

This book presents a selection of the most recent algorithmic advances in Riemannian geometry in the context of machine learning, statistics, optimization, computer vision, and related fields. The unifying theme of the different chapters in the book is the exploitation of the geometry of data using the mathematical machinery of Riemannian geometry. As demonstrated by all the chapters in the book, when the data is intrinsically non-Euclidean, the utilization of this geometrical information can lead to better algorithms that can

### Optimization Algorithms on Matrix Manifolds

- Author : P.-A. Absil,R. Mahony,R. Sepulchre
- Publisher : Princeton University Press
- Release Date : 2009-04-11
- ISBN : 1400830249

Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It places careful emphasis on both the numerical formulation of the algorithm and its differential geometric abstraction--illustrating how good algorithms draw equally from the insights of differential geometry, optimization, and numerical analysis. Two more theoretical chapters provide readers with the

### Recent Advances in Optimization and its Applications in Engineering

- Author : Moritz Diehl,Francois Glineur,Elias Jarlebring,Wim Michiels
- Publisher : Springer Science & Business Media
- Release Date : 2010-09-21
- ISBN : 9783642125980

Mathematical optimization encompasses both a rich and rapidly evolving body of fundamental theory, and a variety of exciting applications in science and engineering. The present book contains a careful selection of articles on recent advances in optimization theory, numerical methods, and their applications in engineering. It features in particular new methods and applications in the fields of optimal control, PDE-constrained optimization, nonlinear optimization, and convex optimization. The authors of this volume took part in the 14th Belgian-French-German Conference on Optimization (

### Nonsmooth Optimization and Its Applications

- Author : Seyedehsomayeh Hosseini,Boris S. Mordukhovich,André Uschmajew
- Publisher : Unknown
- Release Date : 2019
- ISBN : 303011371X

Since nonsmooth optimization problems arise in a diverse range of real-world applications, the potential impact of efficient methods for solving such problems is undeniable. Even solving difficult smooth problems sometimes requires the use of nonsmooth optimization methods, in order to either reduce the problem's scale or simplify its structure. Accordingly, the field of nonsmooth optimization is an important area of mathematical programming that is based on by now classical concepts of variational analysis and generalized derivatives, and has developed a

### Optimization and Its Applications in Control and Data Sciences

- Author : Boris Goldengorin
- Publisher : Springer
- Release Date : 2016-09-29
- ISBN : 9783319420561

This book focuses on recent research in modern optimization and its implications in control and data analysis. This book is a collection of papers from the conference “Optimization and Its Applications in Control and Data Science” dedicated to Professor Boris T. Polyak, which was held in Moscow, Russia on May 13-15, 2015. This book reflects developments in theory and applications rooted by Professor Polyak’s fundamental contributions to constrained and unconstrained optimization, differentiable and nonsmooth functions, control theory and approximation. Each

### Population-Based Optimization on Riemannian Manifolds

- Author : Robert Simon Fong
- Publisher : Springer Nature
- Release Date : 2022-05-29
- ISBN : 9783031042935

### Geometric Science of Information

- Author : Frank Nielsen,Frédéric Barbaresco
- Publisher : Springer
- Release Date : 2013-08-19
- ISBN : 9783642400209

This book constitutes the refereed proceedings of the First International Conference on Geometric Science of Information, GSI 2013, held in Paris, France, in August 2013. The nearly 100 papers presented were carefully reviewed and selected from numerous submissions and are organized into the following thematic sessions: Geometric Statistics on Manifolds and Lie Groups, Deformations in Shape Spaces, Differential Geometry in Signal Processing, Relational Metric, Discrete Metric Spaces, Computational Information Geometry, Hessian Information Geometry I and II, Computational Aspects of Information Geometry in Statistics,

### Information Geometry and Its Applications

- Author : Shun-ichi Amari
- Publisher : Springer
- Release Date : 2016-02-02
- ISBN : 9784431559788

This is the first comprehensive book on information geometry, written by the founder of the field. It begins with an elementary introduction to dualistic geometry and proceeds to a wide range of applications, covering information science, engineering, and neuroscience. It consists of four parts, which on the whole can be read independently. A manifold with a divergence function is first introduced, leading directly to dualistic structure, the heart of information geometry. This part (Part I) can be apprehended without any

### Nonsmooth Optimization

- Author : Marko M Mäkelä,Pekka Neittaanmäki
- Publisher : World Scientific
- Release Date : 1992-05-07
- ISBN : 9789814522410

This book is a self-contained elementary study for nonsmooth analysis and optimization, and their use in solution of nonsmooth optimal control problems. The first part of the book is concerned with nonsmooth differential calculus containing necessary tools for nonsmooth optimization. The second part is devoted to the methods of nonsmooth optimization and their development. A proximal bundle method for nonsmooth nonconvex optimization subject to nonsmooth constraints is constructed. In the last part nonsmooth optimization is applied to problems arising from

### Differential Geometry and Lie Groups

- Author : Jean Gallier,Jocelyn Quaintance
- Publisher : Springer Nature
- Release Date : 2020-08-14
- ISBN : 9783030460402

This textbook offers an introduction to differential geometry designed for readers interested in modern geometry processing. Working from basic undergraduate prerequisites, the authors develop manifold theory and Lie groups from scratch; fundamental topics in Riemannian geometry follow, culminating in the theory that underpins manifold optimization techniques. Students and professionals working in computer vision, robotics, and machine learning will appreciate this pathway into the mathematical concepts behind many modern applications. Starting with the matrix exponential, the text begins with an introduction

### Ultra-Dense Networks

- Author : Haijun Zhang,Jemin Lee,Tony Q. S. Quek,Chih-Lin I
- Publisher : Cambridge University Press
- Release Date : 2020-09-30
- ISBN : 9781108497930

Understand the theory, key technologies and applications of UDNs with this authoritative survey.

### Proceedings

- Author : Anonim
- Publisher : Presses universitaires de Louvain
- Release Date : 2015
- ISBN : 9782875870155