Minimum Volume Ellipsoids
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Minimum-Volume Ellipsoids
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
Author: Stephen P. Boyd
language: en
Publisher: Cambridge University Press
Release Date: 2004-03-08
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.
New Results and New Trends in Computer Science
Author: Hermann Maurer
language: en
Publisher: Springer Science & Business Media
Release Date: 1991-11-13
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.