Minimum Volume Ellipsoids
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Minimum Volume Ellipsoids
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Author : Michael J. Todd
language : en
Publisher: SIAM
Release Date : 2016-07-11
Minimum Volume Ellipsoids written by Michael J. Todd and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-11 with Mathematics categories.
This book, the first on these topics, addresses the problem of finding an ellipsoid to represent a large set of points in high-dimensional space, which has applications in computational geometry, data representations, and optimal design in statistics. The book covers the formulation of this and related problems, theoretical properties of their optimal solutions, and algorithms for their solution. Due to the high dimensionality of these problems, first-order methods that require minimal computational work at each iteration are attractive. While algorithms of this kind have been discovered and rediscovered over the past fifty years, their computational complexities and convergence rates have only recently been investigated. The optimization problems in the book have the entries of a symmetric matrix as their variables, so the author's treatment also gives an introduction to recent work in matrix optimization. This book provides historical perspective on the problems studied by optimizers, statisticians, and geometric functional analysts; demonstrates the huge computational savings possible by exploiting simple updates for the determinant and the inverse after a rank-one update, and highlights the difficulties in algorithms when related problems are studied that do not allow simple updates at each iteration; and gives rigorous analyses of the proposed algorithms, MATLAB codes, and computational results.
Convex Optimization
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Author : Stephen P. Boyd
language : en
Publisher: Cambridge University Press
Release Date : 2004-03-08
Convex Optimization written by Stephen P. Boyd and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-08 with Business & Economics categories.
Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.
Innovations In Bio Inspired Computing And Applications
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Author : Ajith Abraham
language : en
Publisher: Springer Nature
Release Date : 2021-04-09
Innovations In Bio Inspired Computing And Applications written by Ajith Abraham and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-09 with Technology & Engineering categories.
This book highlights recent research on bio-inspired computing and its various innovative applications in information and communication technologies. It presents 51 high-quality papers from the 11th International Conference on Innovations in Bio-Inspired Computing and Applications (IBICA 2020) and 10th World Congress on Information and Communication Technologies (WICT 2020), which was held online during December 16–18, 2019. As a premier conference, IBICA–WICT brings together researchers, engineers and practitioners whose work involves bio-inspired computing, computational intelligence and their applications in information security, real-world contexts, etc. Including contributions by authors from 25 countries, the book offers a valuable reference guide for all researchers, students and practitioners in the fields of Computer Science and Engineering.
New Results And New Trends In Computer Science
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Author : Hermann Maurer
language : en
Publisher: Springer Science & Business Media
Release Date : 1991-11-13
New Results And New Trends In Computer Science written by Hermann Maurer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-11-13 with Computers categories.
This volume contains selected papers from the symposium "New Results and NewTrends in Computer Science" held in Graz, Austria, June 20-21, 1991. The symposium was organized to give a wide-ranging overview of new work in the field on the occasion of the fiftieth birthday of the editor of the volume. Topics covered include: information on neural nets, ideas on a new paradigm for informatics, hypermedia systems and applications, axioms for concurrent processes, techniques for image generation and compression, the role of data visualization, object-oriented programming andgraphics, algorithms for layout compaction, new methods in database systems, the future of data networks, object-oriented artificial intelligence, problems in data structures and sorting, aspects of user interfaces, a theory of structures, applications of cryptography, evaluation of Ada, results in algorithmic geometry, remarks on the history of computers, and a novel interpretation of machine learning. In total, the 26 high-level contributions authored by prominent experts from all over the world give an up-to-date survey of almost all subfields of computer science. The book is written in a style which is easy to follow, and it is of interest for any computer scientist, be it in research, teaching or practice.
Introduction To Robust Estimation And Hypothesis Testing
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Author : Rand R. Wilcox
language : en
Publisher: Academic Press
Release Date : 2005-01-05
Introduction To Robust Estimation And Hypothesis Testing written by Rand R. Wilcox and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-05 with Mathematics categories.
This revised book provides a thorough explanation of the foundation of robust methods, incorporating the latest updates on R and S-Plus, robust ANOVA (Analysis of Variance) and regression. It guides advanced students and other professionals through the basic strategies used for developing practical solutions to problems, and provides a brief background on the foundations of modern methods, placing the new methods in historical context. Author Rand Wilcox includes chapter exercises and many real-world examples that illustrate how various methods perform in different situations. Introduction to Robust Estimation and Hypothesis Testing, Second Edition, focuses on the practical applications of modern, robust methods which can greatly enhance our chances of detecting true differences among groups and true associations among variables. * Covers latest developments in robust regression * Covers latest improvements in ANOVA * Includes newest rank-based methods * Describes and illustrated easy to use software
Optimization Models
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Author : Giuseppe C. Calafiore
language : en
Publisher: Cambridge University Press
Release Date : 2014-10-31
Optimization Models written by Giuseppe C. Calafiore and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-31 with Business & Economics categories.
This accessible textbook demonstrates how to recognize, simplify, model and solve optimization problems - and apply these principles to new projects.
Banach Space Theory
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Author : Marián Fabian
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-04
Banach Space Theory written by Marián Fabian and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-04 with Mathematics categories.
Banach spaces provide a framework for linear and nonlinear functional analysis, operator theory, abstract analysis, probability, optimization and other branches of mathematics. This book introduces the reader to linear functional analysis and to related parts of infinite-dimensional Banach space theory. Key Features: - Develops classical theory, including weak topologies, locally convex space, Schauder bases and compact operator theory - Covers Radon-Nikodým property, finite-dimensional spaces and local theory on tensor products - Contains sections on uniform homeomorphisms and non-linear theory, Rosenthal's L1 theorem, fixed points, and more - Includes information about further topics and directions of research and some open problems at the end of each chapter - Provides numerous exercises for practice The text is suitable for graduate courses or for independent study. Prerequisites include basic courses in calculus and linear. Researchers in functional analysis will also benefit for this book as it can serve as a reference book.
Quasiconvex Optimization And Location Theory
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Author : J.A. dos Santos Gromicho
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Quasiconvex Optimization And Location Theory written by J.A. dos Santos Gromicho and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
grams of which the objective is given by the ratio of a convex by a positive (over a convex domain) concave function. As observed by Sniedovich (Ref. [102, 103]) most of the properties of fractional pro grams could be found in other programs, given that the objective function could be written as a particular composition of functions. He called this new field C programming, standing for composite concave programming. In his seminal book on dynamic programming (Ref. [104]), Sniedovich shows how the study of such com positions can help tackling non-separable dynamic programs that otherwise would defeat solution. Barros and Frenk (Ref. [9]) developed a cutting plane algorithm capable of optimizing C-programs. More recently, this algorithm has been used by Carrizosa and Plastria to solve a global optimization problem in facility location (Ref. [16]). The distinction between global optimization problems (Ref. [54]) and generalized convex problems can sometimes be hard to establish. That is exactly the reason why so much effort has been placed into finding an exhaustive classification of the different weak forms of convexity, establishing a new definition just to satisfy some desirable property in the most general way possible. This book does not aim at all the subtleties of the different generalizations of convexity, but concentrates on the most general of them all, quasiconvex programming. Chapter 5 shows clearly where the real difficulties appear.
Lectures On Discrete Geometry
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Author : Ji?í Matoušek
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-05-02
Lectures On Discrete Geometry written by Ji?í Matoušek and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-05-02 with Mathematics categories.
The main topics in this introductory text to discrete geometry include basics on convex sets, convex polytopes and hyperplane arrangements, combinatorial complexity of geometric configurations, intersection patterns and transversals of convex sets, geometric Ramsey-type results, and embeddings of finite metric spaces into normed spaces. In each area, the text explains several key results and methods.
Visualizing Statistical Models And Concepts
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Author : R.W. Farebrother
language : en
Publisher: CRC Press
Release Date : 2002-06-14
Visualizing Statistical Models And Concepts written by R.W. Farebrother and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-06-14 with Mathematics categories.
Examines classic algorithms, geometric diagrams, and mechanical principles for enhancing visualization of statistical estimation procedures and mathematical concepts in physics, engineering, and computer programming.