Sparse Optimization Theory and Methods - 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 Sparse Optimization Theory and Methods write by Yun-Bin Zhao. This book was released on 2018-07-04. Sparse Optimization Theory and Methods available in PDF, EPUB and Kindle. Seeking sparse solutions of underdetermined linear systems is required in many areas of engineering and science such as signal and image processing. The efficient sparse representation becomes central in various big or high-dimensional data processing, yielding fruitful theoretical and realistic results in these fields. The mathematical optimization plays a fundamentally important role in the development of these results and acts as the mainstream numerical algorithms for the sparsity-seeking problems arising from big-data processing, compressed sensing, statistical learning, computer vision, and so on. This has attracted the interest of many researchers at the interface of engineering, mathematics and computer science. Sparse Optimization Theory and Methods presents the state of the art in theory and algorithms for signal recovery under the sparsity assumption. The up-to-date uniqueness conditions for the sparsest solution of underdertemined linear systems are described. The results for sparse signal recovery under the matrix property called range space property (RSP) are introduced, which is a deep and mild condition for the sparse signal to be recovered by convex optimization methods. This framework is generalized to 1-bit compressed sensing, leading to a novel sign recovery theory in this area. Two efficient sparsity-seeking algorithms, reweighted l1-minimization in primal space and the algorithm based on complementary slackness property, are presented. The theoretical efficiency of these algorithms is rigorously analysed in this book. Under the RSP assumption, the author also provides a novel and unified stability analysis for several popular optimization methods for sparse signal recovery, including l1-mininization, Dantzig selector and LASSO. This book incorporates recent development and the author’s latest research in the field that have not appeared in other books.
Sparsity Methods for Systems and Control
Sparsity Methods for Systems and Control - 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 Sparsity Methods for Systems and Control write by Masaaki Nagahara. This book was released on 2020-09-30. Sparsity Methods for Systems and Control available in PDF, EPUB and Kindle. The method of sparsity has been attracting a lot of attention in the fields related not only to signal processing, machine learning, and statistics, but also systems and control. The method is known as compressed sensing, compressive sampling, sparse representation, or sparse modeling. More recently, the sparsity method has been applied to systems and control to design resource-aware control systems. This book gives a comprehensive guide to sparsity methods for systems and control, from standard sparsity methods in finite-dimensional vector spaces (Part I) to optimal control methods in infinite-dimensional function spaces (Part II). The primary objective of this book is to show how to use sparsity methods for several engineering problems. For this, the author provides MATLAB programs by which the reader can try sparsity methods for themselves. Readers will obtain a deep understanding of sparsity methods by running these MATLAB programs. Sparsity Methods for Systems and Control is suitable for graduate level university courses, though it should also be comprehendible to undergraduate students who have a basic knowledge of linear algebra and elementary calculus. Also, especially part II of the book should appeal to professional researchers and engineers who are interested in applying sparsity methods to systems and control.
Practical Methods for Optimal Control and Estimation Using Nonlinear Programming
Practical Methods for Optimal Control and Estimation Using Nonlinear Programming - 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 Practical Methods for Optimal Control and Estimation Using Nonlinear Programming write by John T. Betts. This book was released on 2010-01-01. Practical Methods for Optimal Control and Estimation Using Nonlinear Programming available in PDF, EPUB and Kindle. A focused presentation of how sparse optimization methods can be used to solve optimal control and estimation problems.
Sparse Polynomial Optimization: Theory And Practice
Sparse Polynomial Optimization: Theory And Practice - 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 Sparse Polynomial Optimization: Theory And Practice write by Victor Magron. This book was released on 2023-04-25. Sparse Polynomial Optimization: Theory And Practice available in PDF, EPUB and Kindle. Many applications, including computer vision, computer arithmetic, deep learning, entanglement in quantum information, graph theory and energy networks, can be successfully tackled within the framework of polynomial optimization, an emerging field with growing research efforts in the last two decades. One key advantage of these techniques is their ability to model a wide range of problems using optimization formulations. Polynomial optimization heavily relies on the moment-sums of squares (moment-SOS) approach proposed by Lasserre, which provides certificates for positive polynomials. On the practical side, however, there is 'no free lunch' and such optimization methods usually encompass severe scalability issues. Fortunately, for many applications, including the ones formerly mentioned, we can look at the problem in the eyes and exploit the inherent data structure arising from the cost and constraints describing the problem.This book presents several research efforts to resolve this scientific challenge with important computational implications. It provides the development of alternative optimization schemes that scale well in terms of computational complexity, at least in some identified class of problems. It also features a unified modeling framework to handle a wide range of applications involving both commutative and noncommutative variables, and to solve concretely large-scale instances. Readers will find a practical section dedicated to the use of available open-source software libraries.This interdisciplinary monograph is essential reading for students, researchers and professionals interested in solving optimization problems with polynomial input data.
Optimization Theory and Methods
Optimization Theory and Methods - 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 Optimization Theory and Methods write by Wenyu Sun. This book was released on 2006-08-06. Optimization Theory and Methods available in PDF, EPUB and Kindle. Optimization Theory and Methods can be used as a textbook for an optimization course for graduates and senior undergraduates. It is the result of the author's teaching and research over the past decade. It describes optimization theory and several powerful methods. For most methods, the book discusses an idea’s motivation, studies the derivation, establishes the global and local convergence, describes algorithmic steps, and discusses the numerical performance.
