Proximal Algorithms - 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 Proximal Algorithms write by Neal Parikh. This book was released on 2013-11. Proximal Algorithms available in PDF, EPUB and Kindle. Proximal Algorithms discusses proximal operators and proximal algorithms, and illustrates their applicability to standard and distributed convex optimization in general and many applications of recent interest in particular. Much like Newton's method is a standard tool for solving unconstrained smooth optimization problems of modest size, proximal algorithms can be viewed as an analogous tool for nonsmooth, constrained, large-scale, or distributed versions of these problems. They are very generally applicable, but are especially well-suited to problems of substantial recent interest involving large or high-dimensional datasets. Proximal methods sit at a higher level of abstraction than classical algorithms like Newton's method: the base operation is evaluating the proximal operator of a function, which itself involves solving a small convex optimization problem. These subproblems, which generalize the problem of projecting a point onto a convex set, often admit closed-form solutions or can be solved very quickly with standard or simple specialized methods. Proximal Algorithms discusses different interpretations of proximal operators and algorithms, looks at their connections to many other topics in optimization and applied mathematics, surveys some popular algorithms, and provides a large number of examples of proximal operators that commonly arise in practice.
Splitting Algorithms, Modern Operator Theory, and Applications
Splitting Algorithms, Modern Operator Theory, 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 Splitting Algorithms, Modern Operator Theory, and Applications write by Heinz H. Bauschke. This book was released on 2019-11-06. Splitting Algorithms, Modern Operator Theory, and Applications available in PDF, EPUB and Kindle. 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.
Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging
Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging - 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 Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging write by Ke Chen. This book was released on 2023-02-24. Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging available in PDF, EPUB and Kindle. This handbook gathers together the state of the art on mathematical models and algorithms for imaging and vision. Its emphasis lies on rigorous mathematical methods, which represent the optimal solutions to a class of imaging and vision problems, and on effective algorithms, which are necessary for the methods to be translated to practical use in various applications. Viewing discrete images as data sampled from functional surfaces enables the use of advanced tools from calculus, functions and calculus of variations, and nonlinear optimization, and provides the basis of high-resolution imaging through geometry and variational models. Besides, optimization naturally connects traditional model-driven approaches to the emerging data-driven approaches of machine and deep learning. No other framework can provide comparable accuracy and precision to imaging and vision. Written by leading researchers in imaging and vision, the chapters in this handbook all start with gentle introductions, which make this work accessible to graduate students. For newcomers to the field, the book provides a comprehensive and fast-track introduction to the content, to save time and get on with tackling new and emerging challenges. For researchers, exposure to the state of the art of research works leads to an overall view of the entire field so as to guide new research directions and avoid pitfalls in moving the field forward and looking into the next decades of imaging and information services. This work can greatly benefit graduate students, researchers, and practitioners in imaging and vision; applied mathematicians; medical imagers; engineers; and computer scientists.
Splitting Methods in Communication, Imaging, Science, and Engineering
Splitting Methods in Communication, Imaging, Science, and 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 Splitting Methods in Communication, Imaging, Science, and Engineering write by Roland Glowinski. This book was released on 2017-01-05. Splitting Methods in Communication, Imaging, Science, and Engineering available in PDF, EPUB and Kindle. This book is about computational methods based on operator splitting. It consists of twenty-three chapters written by recognized splitting method contributors and practitioners, and covers a vast spectrum of topics and application areas, including computational mechanics, computational physics, image processing, wireless communication, nonlinear optics, and finance. Therefore, the book presents very versatile aspects of splitting methods and their applications, motivating the cross-fertilization of ideas.
Algorithms for Solving Common Fixed Point Problems
Algorithms for Solving Common Fixed Point Problems - 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 Algorithms for Solving Common Fixed Point Problems write by Alexander J. Zaslavski. This book was released on 2018-05-02. Algorithms for Solving Common Fixed Point Problems available in PDF, EPUB and Kindle. This book details approximate solutions to common fixed point problems and convex feasibility problems in the presence of perturbations. Convex feasibility problems search for a common point of a finite collection of subsets in a Hilbert space; common fixed point problems pursue a common fixed point of a finite collection of self-mappings in a Hilbert space. A variety of algorithms are considered in this book for solving both types of problems, the study of which has fueled a rapidly growing area of research. This monograph is timely and highlights the numerous applications to engineering, computed tomography, and radiation therapy planning. Totaling eight chapters, this book begins with an introduction to foundational material and moves on to examine iterative methods in metric spaces. The dynamic string-averaging methods for common fixed point problems in normed space are analyzed in Chapter 3. Dynamic string methods, for common fixed point problems in a metric space are introduced and discussed in Chapter 4. Chapter 5 is devoted to the convergence of an abstract version of the algorithm which has been called component-averaged row projections (CARP). Chapter 6 studies a proximal algorithm for finding a common zero of a family of maximal monotone operators. Chapter 7 extends the results of Chapter 6 for a dynamic string-averaging version of the proximal algorithm. In Chapters 8 subgradient projections algorithms for convex feasibility problems are examined for infinite dimensional Hilbert spaces.
