Riemannian Optimization and Its Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Riemannian Optimization and Its Applications write by Hiroyuki Sato. This book was released on 2021-02-17. Riemannian Optimization and Its Applications available 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.
Convex Functions and Optimization Methods on Riemannian Manifolds
Convex Functions and Optimization Methods on Riemannian Manifolds - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Convex Functions and Optimization Methods on Riemannian Manifolds write by C. Udriste. This book was released on 2013-11-11. Convex Functions and Optimization Methods on Riemannian Manifolds available in PDF, EPUB and Kindle. 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; Geometric examples of convex functions; Flows, convexity and energies; Semidefinite Hessians and applications; Minimization of functions on Riemannian manifolds. All the numerical algorithms, computer programs and the appendices (Riemannian convexity of functions f:R ~ R, Descent methods on the Poincare plane, Descent methods on the sphere, Completeness and convexity on Finsler manifolds) constitute an attempt to make accesible to all users of this book some basic computational techniques and implementation of geometric structures. To further aid the readers,this book also contains a part of the folklore about Riemannian geometry, convex functions and dynamical systems because it is unfortunately "nowhere" to be found in the same context; existing textbooks on convex functions on Euclidean spaces or on dynamical systems do not mention what happens in Riemannian geometry, while the papers dealing with Riemannian manifolds usually avoid discussing elementary facts. Usually a convex function on a Riemannian manifold is a real valued function whose restriction to every geodesic arc is convex.
Algorithmic Advances in Riemannian Geometry and Applications
Algorithmic Advances in Riemannian Geometry and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algorithmic Advances in Riemannian Geometry and Applications write by Hà Quang Minh. This book was released on 2016-10-05. Algorithmic Advances in Riemannian Geometry and Applications available in PDF, EPUB and Kindle. 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 capture more accurately the structures inherent in the data, leading ultimately to better empirical performance. This book is not intended to be an encyclopedic compilation of the applications of Riemannian geometry. Instead, it focuses on several important research directions that are currently actively pursued by researchers in the field. These include statistical modeling and analysis on manifolds,optimization on manifolds, Riemannian manifolds and kernel methods, and dictionary learning and sparse coding on manifolds. Examples of applications include novel algorithms for Monte Carlo sampling and Gaussian Mixture Model fitting, 3D brain image analysis,image classification, action recognition, and motion tracking.
Nonsmooth Optimization and Its Applications
Nonsmooth Optimization and Its Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonsmooth Optimization and Its Applications write by Seyedehsomayeh Hosseini. This book was released on 2019-03-29. Nonsmooth Optimization and Its Applications available in PDF, EPUB and Kindle. 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 rich and sophisticated set of mathematical tools at the intersection of theory and practice. This volume of ISNM is an outcome of the workshop "Nonsmooth Optimization and its Applications," which was held from May 15 to 19, 2017 at the Hausdorff Center for Mathematics, University of Bonn. The six research articles gathered here focus on recent results that highlight different aspects of nonsmooth and variational analysis, optimization methods, their convergence theory and applications.
Recent Advances in Optimization and its Applications in Engineering
Recent Advances in Optimization and its Applications in Engineering - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Recent Advances in Optimization and its Applications in Engineering write by Moritz Diehl. This book was released on 2010-09-21. Recent Advances in Optimization and its Applications in Engineering available in PDF, EPUB and Kindle. 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 (BFG09) organized in Leuven, Belgium, on September 14-18, 2009. The volume contains a selection of reviewed articles contributed by the conference speakers as well as three survey articles by plenary speakers and two papers authored by the winners of the best talk and best poster prizes awarded at BFG09. Researchers and graduate students in applied mathematics, computer science, and many branches of engineering will find in this book an interesting and useful collection of recent ideas on the methods and applications of optimization.
