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Convergence Of Gradient Like Dynamical Systems And Optimization Algorithms
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Book Synopsis Optimization and Dynamical Systems by : Uwe Helmke
Download or read book Optimization and Dynamical Systems written by Uwe Helmke and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is aimed at mathematics and engineering graduate students and researchers in the areas of optimization, dynamical systems, control sys tems, signal processing, and linear algebra. The motivation for the results developed here arises from advanced engineering applications and the emer gence of highly parallel computing machines for tackling such applications. The problems solved are those of linear algebra and linear systems the ory, and include such topics as diagonalizing a symmetric matrix, singular value decomposition, balanced realizations, linear programming, sensitivity minimization, and eigenvalue assignment by feedback control. The tools are those, not only of linear algebra and systems theory, but also of differential geometry. The problems are solved via dynamical sys tems implementation, either in continuous time or discrete time , which is ideally suited to distributed parallel processing. The problems tackled are indirectly or directly concerned with dynamical systems themselves, so there is feedback in that dynamical systems are used to understand and optimize dynamical systems. One key to the new research results has been the recent discovery of rather deep existence and uniqueness results for the solution of certain matrix least squares optimization problems in geomet ric invariant theory. These problems, as well as many other optimization problems arising in linear algebra and systems theory, do not always admit solutions which can be found by algebraic methods.
Book Synopsis Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) by : Boyan Sirakov
Download or read book Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) written by Boyan Sirakov and published by World Scientific. This book was released on 2019-02-27 with total page 5393 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
Book Synopsis Lagrangian and Hamiltonian Methods For Nonlinear Control 2006 by : Francesco Bullo
Download or read book Lagrangian and Hamiltonian Methods For Nonlinear Control 2006 written by Francesco Bullo and published by Springer. This book was released on 2007-10-06 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Design of Distributed and Robust Optimization Algorithms. A Systems Theoretic Approach by : Simon Michalowsky
Download or read book Design of Distributed and Robust Optimization Algorithms. A Systems Theoretic Approach written by Simon Michalowsky and published by Logos Verlag Berlin GmbH. This book was released on 2020-04-17 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization algorithms are the backbone of many modern technologies. In this thesis, we address the analysis and design of optimization algorithms from a systems theoretic viewpoint. By properly recasting the algorithm design as a controller synthesis problem, we derive methods that enable a systematic design of tailored optimization algorithms. We consider two specific classes of optimization algorithms: (i) distributed, and (ii) robust optimization algorithms. Concerning (i), we utilize ideas from geometric control in an innovative fashion to derive a novel methodology that enables the design of distributed optimization algorithms under minimal assumptions on the graph topology and the structure of the optimization problem. Concerning (ii), we employ robust control techniques to establish a framework for the analysis of existing algorithms as well as the design of novel robust optimization algorithms with specified guarantees.
Book Synopsis Splitting Algorithms, Modern Operator Theory, and Applications by : Heinz H. Bauschke
Download or read book Splitting Algorithms, Modern Operator Theory, and Applications written by Heinz H. Bauschke and published by Springer Nature. This book was released on 2019-11-06 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together research articles and state-of-the-art surveys in broad areas of optimization and numerical analysis with particular emphasis on algorithms. The discussion also focuses on advances in monotone operator theory and other topics from variational analysis and nonsmooth optimization, especially as they pertain to algorithms and concrete, implementable methods. The theory of monotone operators is a central framework for understanding and analyzing splitting algorithms. Topics discussed in the volume were presented at the interdisciplinary workshop titled Splitting Algorithms, Modern Operator Theory, and Applications held in Oaxaca, Mexico in September, 2017. Dedicated to Jonathan M. Borwein, one of the most versatile mathematicians in contemporary history, this compilation brings theory together with applications in novel and insightful ways.
Book Synopsis Generalized Functions, Operator Theory, and Dynamical Systems by : Ioannis Antoniou
Download or read book Generalized Functions, Operator Theory, and Dynamical Systems written by Ioannis Antoniou and published by CRC Press. This book was released on 2021-02-25 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nobel prize winner Ilya Prigogine writes in his preface: "Irreversibility is a challenge to mathematics...[which] leads to generalized functions and to an extension of spectral analysis beyond the conventional Hilbert space theory." Meeting this challenge required new mathematical formulations-obstacles met and largely overcome thanks primarily to the contributors to this volume." This compilation of works grew out of material presented at the "Hyperfunctions, Operator Theory and Dynamical Systems" symposium at the International Solvay Institutes for Physics and Chemistry in 1997. The result is a coherently organized collective work that moves from general, widely applicable mathematical methods to ever more specialized physical applications. Presented in two sections, part one describes Generalized Functions and Operator Theory, part two addresses Operator Theory and Dynamical Systems. The interplay between mathematics and physics is now more necessary than ever-and more difficult than ever, given the increasing complexity of theories and methods.
Book Synopsis Nonsmooth Optimization and Its Applications by : Seyedehsomayeh Hosseini
Download or read book Nonsmooth Optimization and Its Applications written by Seyedehsomayeh Hosseini and published by Springer. This book was released on 2019-03-29 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Dynamical Systems and Numerical Analysis by : Andrew Stuart
Download or read book Dynamical Systems and Numerical Analysis written by Andrew Stuart and published by Cambridge University Press. This book was released on 1998-11-28 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first three chapters contain the elements of the theory of dynamical systems and the numerical solution of initial-value problems. In the remaining chapters, numerical methods are formulated as dynamical systems and the convergence and stability properties of the methods are examined.
Book Synopsis Cooperative Coordination and Formation Control for Multi-agent Systems by : Zhiyong Sun
Download or read book Cooperative Coordination and Formation Control for Multi-agent Systems written by Zhiyong Sun and published by Springer. This book was released on 2018-02-23 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: The thesis presents new results on multi-agent formation control, focusing on the distributed stabilization control of rigid formation shapes. It analyzes a range of current research problems such as problems concerning the equilibrium and stability of formation control systems, or the problem of cooperative coordination control when agents have general dynamical models, and discusses practical considerations arising during the implementation of established formation control algorithms. In addition, the thesis presents models of increasing complexity, from single integrator models, to double integrator models, to agents modeled by nonlinear kinematic and dynamic equations, including the familiar unicycle model and nonlinear system equations with drift terms. Presenting the fruits of a close collaboration between several top control groups at leading universities including Yale University, Groningen University, Purdue University and Gwangju Institute of Science and Technology (GIST), the thesis spans various research areas, including robustness issues in formations, quantization-based coordination, exponential stability in formation systems, and cooperative coordination of networked heterogeneous systems.
Book Synopsis Advances in Dynamics, Optimization and Computation by : Oliver Junge
Download or read book Advances in Dynamics, Optimization and Computation written by Oliver Junge and published by Springer Nature. This book was released on 2020-07-20 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a collection of papers on recent advances in problems concerning dynamics, optimal control and optimization. In many chapters, computational techniques play a central role. Set-oriented techniques feature prominently throughout the book, yielding state-of-the-art algorithms for computing general invariant sets, constructing globally optimal controllers and solving multi-objective optimization problems.
Book Synopsis Convex Optimization Algorithms by : Dimitri Bertsekas
Download or read book Convex Optimization Algorithms written by Dimitri Bertsekas and published by Athena Scientific. This book was released on 2015-02-01 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive and accessible presentation of algorithms for solving convex optimization problems. It relies on rigorous mathematical analysis, but also aims at an intuitive exposition that makes use of visualization where possible. This is facilitated by the extensive use of analytical and algorithmic concepts of duality, which by nature lend themselves to geometrical interpretation. The book places particular emphasis on modern developments, and their widespread applications in fields such as large-scale resource allocation problems, signal processing, and machine learning. The book is aimed at students, researchers, and practitioners, roughly at the first year graduate level. It is similar in style to the author's 2009"Convex Optimization Theory" book, but can be read independently. The latter book focuses on convexity theory and optimization duality, while the present book focuses on algorithmic issues. The two books share notation, and together cover the entire finite-dimensional convex optimization methodology. To facilitate readability, the statements of definitions and results of the "theory book" are reproduced without proofs in Appendix B.
Book Synopsis Optimization Algorithms on Matrix Manifolds by : P.-A. Absil
Download or read book Optimization Algorithms on Matrix Manifolds written by P.-A. Absil and published by Princeton University Press. This book was released on 2009-04-11 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 background in differential geometry necessary to algorithmic development. In the other chapters, several well-known optimization methods such as steepest descent and conjugate gradients are generalized to abstract manifolds. The book provides a generic development of each of these methods, building upon the material of the geometric chapters. It then guides readers through the calculations that turn these geometrically formulated methods into concrete numerical algorithms. The state-of-the-art algorithms given as examples are competitive with the best existing algorithms for a selection of eigenspace problems in numerical linear algebra. Optimization Algorithms on Matrix Manifolds offers techniques with broad applications in linear algebra, signal processing, data mining, computer vision, and statistical analysis. It can serve as a graduate-level textbook and will be of interest to applied mathematicians, engineers, and computer scientists.
Book Synopsis Control Perspectives on Numerical Algorithms and Matrix Problems by : Amit Bhaya
Download or read book Control Perspectives on Numerical Algorithms and Matrix Problems written by Amit Bhaya and published by SIAM. This book was released on 2006-03-01 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book organizes the analysis and design of iterative numerical methods from a control perspective. A variety of applications are discussed, including iterative methods for linear and nonlinear systems of equations, neural networks for linear and quadratic programming problems and integration and shooting methods for ordinary differential equations.
Book Synopsis Statistical Machine Learning by : Richard Golden
Download or read book Statistical Machine Learning written by Richard Golden and published by CRC Press. This book was released on 2020-06-24 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: The recent rapid growth in the variety and complexity of new machine learning architectures requires the development of improved methods for designing, analyzing, evaluating, and communicating machine learning technologies. Statistical Machine Learning: A Unified Framework provides students, engineers, and scientists with tools from mathematical statistics and nonlinear optimization theory to become experts in the field of machine learning. In particular, the material in this text directly supports the mathematical analysis and design of old, new, and not-yet-invented nonlinear high-dimensional machine learning algorithms. Features: Unified empirical risk minimization framework supports rigorous mathematical analyses of widely used supervised, unsupervised, and reinforcement machine learning algorithms Matrix calculus methods for supporting machine learning analysis and design applications Explicit conditions for ensuring convergence of adaptive, batch, minibatch, MCEM, and MCMC learning algorithms that minimize both unimodal and multimodal objective functions Explicit conditions for characterizing asymptotic properties of M-estimators and model selection criteria such as AIC and BIC in the presence of possible model misspecification This advanced text is suitable for graduate students or highly motivated undergraduate students in statistics, computer science, electrical engineering, and applied mathematics. The text is self-contained and only assumes knowledge of lower-division linear algebra and upper-division probability theory. Students, professional engineers, and multidisciplinary scientists possessing these minimal prerequisites will find this text challenging yet accessible. About the Author: Richard M. Golden (Ph.D., M.S.E.E., B.S.E.E.) is Professor of Cognitive Science and Participating Faculty Member in Electrical Engineering at the University of Texas at Dallas. Dr. Golden has published articles and given talks at scientific conferences on a wide range of topics in the fields of both statistics and machine learning over the past three decades. His long-term research interests include identifying conditions for the convergence of deterministic and stochastic machine learning algorithms and investigating estimation and inference in the presence of possibly misspecified probability models.
Download or read book NASA Technical Paper written by and published by . This book was released on 1984 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Taming Heterogeneity and Complexity of Embedded Control by : Françoise Lamnabhi-Lagarrigu
Download or read book Taming Heterogeneity and Complexity of Embedded Control written by Françoise Lamnabhi-Lagarrigu and published by John Wiley & Sons. This book was released on 2013-05-21 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers together a selection of papers presented at the Joint CTS-HYCON Workshop on Nonlinear and Hybrid Control held at the Paris Sorbonne, France, 10-12 July 2006. The main objective of the Workshop was to promote the exchange of ideas and experiences and reinforce scientific contacts in the large multidisciplinary area of the control of nonlinear and hybrid systems.
Download or read book Dynamical Search written by Luc Pronzato and published by CRC Press. This book was released on 1999-08-27 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Certain algorithms that are known to converge can be renormalized or "blown up" at each iteration so that their local behavior can be seen. This creates dynamical systems that we can study with modern tools, such as ergodic theory, chaos, special attractors, and Lyapounov exponents. Furthermore, we can translate the rates of convergence into less studied exponents known as Renyi entropies. This all feeds back to suggest new algorithms with faster rates of convergence. For example, in line-search, we can improve upon the Golden Section algorithm with new classes of algorithms that have their own special-and sometimes chaotic-dynamical systems. The ellipsoidal algorithms of linear and convex programming have fast, "deep cut" versions whose dynamical systems contain cyclic attractors. And ordinary steepest descent has, buried within, a beautiful fractal that controls the gateway to a special two-point attractor. Faster "relaxed" versions exhibit classical period doubling. Dynamical Search presents a stimulating introduction to a brand new field - the union of dynamical systems and optimization. It will prove fascinating and open doors to new areas of investigation for researchers in both fields, plus those in statistics and computer science.
