Proximal Algorithms

Proximal Algorithms

Author: Neal Parikh

Publisher: Now Pub

Published: 2013-11

Total Pages: 130

ISBN-13: 9781601987167

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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.


Book Synopsis Proximal Algorithms by : Neal Parikh

Download or read book Proximal Algorithms written by Neal Parikh and published by Now Pub. This book was released on 2013-11 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author: Heinz H. Bauschke

Publisher: Springer Nature

Published: 2019-11-06

Total Pages: 489

ISBN-13: 3030259390

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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 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 489 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.

Fixed-Point Algorithms for Inverse Problems in Science and Engineering

Fixed-Point Algorithms for Inverse Problems in Science and Engineering

Author: Heinz H. Bauschke

Publisher: Springer Science & Business Media

Published: 2011-05-27

Total Pages: 409

ISBN-13: 1441995692

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"Fixed-Point Algorithms for Inverse Problems in Science and Engineering" presents some of the most recent work from top-notch researchers studying projection and other first-order fixed-point algorithms in several areas of mathematics and the applied sciences. The material presented provides a survey of the state-of-the-art theory and practice in fixed-point algorithms, identifying emerging problems driven by applications, and discussing new approaches for solving these problems. This book incorporates diverse perspectives from broad-ranging areas of research including, variational analysis, numerical linear algebra, biotechnology, materials science, computational solid-state physics, and chemistry. Topics presented include: Theory of Fixed-point algorithms: convex analysis, convex optimization, subdifferential calculus, nonsmooth analysis, proximal point methods, projection methods, resolvent and related fixed-point theoretic methods, and monotone operator theory. Numerical analysis of fixed-point algorithms: choice of step lengths, of weights, of blocks for block-iterative and parallel methods, and of relaxation parameters; regularization of ill-posed problems; numerical comparison of various methods. Areas of Applications: engineering (image and signal reconstruction and decompression problems), computer tomography and radiation treatment planning (convex feasibility problems), astronomy (adaptive optics), crystallography (molecular structure reconstruction), computational chemistry (molecular structure simulation) and other areas. Because of the variety of applications presented, this book can easily serve as a basis for new and innovated research and collaboration.


Book Synopsis Fixed-Point Algorithms for Inverse Problems in Science and Engineering by : Heinz H. Bauschke

Download or read book Fixed-Point Algorithms for Inverse Problems in Science and Engineering written by Heinz H. Bauschke and published by Springer Science & Business Media. This book was released on 2011-05-27 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Fixed-Point Algorithms for Inverse Problems in Science and Engineering" presents some of the most recent work from top-notch researchers studying projection and other first-order fixed-point algorithms in several areas of mathematics and the applied sciences. The material presented provides a survey of the state-of-the-art theory and practice in fixed-point algorithms, identifying emerging problems driven by applications, and discussing new approaches for solving these problems. This book incorporates diverse perspectives from broad-ranging areas of research including, variational analysis, numerical linear algebra, biotechnology, materials science, computational solid-state physics, and chemistry. Topics presented include: Theory of Fixed-point algorithms: convex analysis, convex optimization, subdifferential calculus, nonsmooth analysis, proximal point methods, projection methods, resolvent and related fixed-point theoretic methods, and monotone operator theory. Numerical analysis of fixed-point algorithms: choice of step lengths, of weights, of blocks for block-iterative and parallel methods, and of relaxation parameters; regularization of ill-posed problems; numerical comparison of various methods. Areas of Applications: engineering (image and signal reconstruction and decompression problems), computer tomography and radiation treatment planning (convex feasibility problems), astronomy (adaptive optics), crystallography (molecular structure reconstruction), computational chemistry (molecular structure simulation) and other areas. Because of the variety of applications presented, this book can easily serve as a basis for new and innovated research and collaboration.

Sparse Modeling

Sparse Modeling

Author: Irina Rish

Publisher: CRC Press

Published: 2014-12-01

Total Pages: 255

ISBN-13: 1439828695

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Sparse models are particularly useful in scientific applications, such as biomarker discovery in genetic or neuroimaging data, where the interpretability of a predictive model is essential. Sparsity can also dramatically improve the cost efficiency of signal processing. Sparse Modeling: Theory, Algorithms, and Applications provides an introduction to the growing field of sparse modeling, including application examples, problem formulations that yield sparse solutions, algorithms for finding such solutions, and recent theoretical results on sparse recovery. The book gets you up to speed on the latest sparsity-related developments and will motivate you to continue learning about the field. The authors first present motivating examples and a high-level survey of key recent developments in sparse modeling. The book then describes optimization problems involving commonly used sparsity-enforcing tools, presents essential theoretical results, and discusses several state-of-the-art algorithms for finding sparse solutions. The authors go on to address a variety of sparse recovery problems that extend the basic formulation to more sophisticated forms of structured sparsity and to different loss functions. They also examine a particular class of sparse graphical models and cover dictionary learning and sparse matrix factorizations.


Book Synopsis Sparse Modeling by : Irina Rish

Download or read book Sparse Modeling written by Irina Rish and published by CRC Press. This book was released on 2014-12-01 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sparse models are particularly useful in scientific applications, such as biomarker discovery in genetic or neuroimaging data, where the interpretability of a predictive model is essential. Sparsity can also dramatically improve the cost efficiency of signal processing. Sparse Modeling: Theory, Algorithms, and Applications provides an introduction to the growing field of sparse modeling, including application examples, problem formulations that yield sparse solutions, algorithms for finding such solutions, and recent theoretical results on sparse recovery. The book gets you up to speed on the latest sparsity-related developments and will motivate you to continue learning about the field. The authors first present motivating examples and a high-level survey of key recent developments in sparse modeling. The book then describes optimization problems involving commonly used sparsity-enforcing tools, presents essential theoretical results, and discusses several state-of-the-art algorithms for finding sparse solutions. The authors go on to address a variety of sparse recovery problems that extend the basic formulation to more sophisticated forms of structured sparsity and to different loss functions. They also examine a particular class of sparse graphical models and cover dictionary learning and sparse matrix factorizations.

Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging

Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging

Author: Ke Chen

Publisher: Springer Nature

Published: 2023-02-24

Total Pages: 1981

ISBN-13: 3030986616

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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.


Book Synopsis Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging by : Ke Chen

Download or read book Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging written by Ke Chen and published by Springer Nature. This book was released on 2023-02-24 with total page 1981 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Scale Space and Variational Methods in Computer Vision

Scale Space and Variational Methods in Computer Vision

Author: Luca Calatroni

Publisher: Springer Nature

Published: 2023-05-09

Total Pages: 767

ISBN-13: 3031319753

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This book constitutes the proceedings of the 9th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2023, which took place in Santa Margherita di Pula, Italy, in May 2023. The 57 papers presented in this volume were carefully reviewed and selected from 72 submissions. They were organized in topical sections as follows: Inverse Problems in Imaging; Machine and Deep Learning in Imaging; Optimization for Imaging: Theory and Methods; Scale Space, PDEs, Flow, Motion and Registration.


Book Synopsis Scale Space and Variational Methods in Computer Vision by : Luca Calatroni

Download or read book Scale Space and Variational Methods in Computer Vision written by Luca Calatroni and published by Springer Nature. This book was released on 2023-05-09 with total page 767 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 9th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2023, which took place in Santa Margherita di Pula, Italy, in May 2023. The 57 papers presented in this volume were carefully reviewed and selected from 72 submissions. They were organized in topical sections as follows: Inverse Problems in Imaging; Machine and Deep Learning in Imaging; Optimization for Imaging: Theory and Methods; Scale Space, PDEs, Flow, Motion and Registration.

Inherently Parallel Algorithms in Feasibility and Optimization and their Applications

Inherently Parallel Algorithms in Feasibility and Optimization and their Applications

Author: D. Butnariu

Publisher: Elsevier

Published: 2001-06-18

Total Pages: 515

ISBN-13: 0080508766

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The Haifa 2000 Workshop on "Inherently Parallel Algorithms for Feasibility and Optimization and their Applications" brought together top scientists in this area. The objective of the Workshop was to discuss, analyze and compare the latest developments in this fast growing field of applied mathematics and to identify topics of research which are of special interest for industrial applications and for further theoretical study. Inherently parallel algorithms, that is, computational methods which are, by their mathematical nature, parallel, have been studied in various contexts for more than fifty years. However, it was only during the last decade that they have mostly proved their practical usefulness because new generations of computers made their implementation possible in order to solve complex feasibility and optimization problems involving huge amounts of data via parallel processing. These led to an accumulation of computational experience and theoretical information and opened new and challenging questions concerning the behavior of inherently parallel algorithms for feasibility and optimization, their convergence in new environments and in circumstances in which they were not considered before their stability and reliability. Several research groups all over the world focused on these questions and it was the general feeling among scientists involved in this effort that the time has come to survey the latest progress and convey a perspective for further development and concerted scientific investigations. Thus, the editors of this volume, with the support of the Israeli Academy for Sciences and Humanities, took the initiative of organizing a Workshop intended to bring together the leading scientists in the field. The current volume is the Proceedings of the Workshop representing the discussions, debates and communications that took place. Having all that information collected in a single book will provide mathematicians and engineers interested in the theoretical and practical aspects of the inherently parallel algorithms for feasibility and optimization with a tool for determining when, where and which algorithms in this class are fit for solving specific problems, how reliable they are, how they behave and how efficient they were in previous applications. Such a tool will allow software creators to choose ways of better implementing these methods by learning from existing experience.


Book Synopsis Inherently Parallel Algorithms in Feasibility and Optimization and their Applications by : D. Butnariu

Download or read book Inherently Parallel Algorithms in Feasibility and Optimization and their Applications written by D. Butnariu and published by Elsevier. This book was released on 2001-06-18 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Haifa 2000 Workshop on "Inherently Parallel Algorithms for Feasibility and Optimization and their Applications" brought together top scientists in this area. The objective of the Workshop was to discuss, analyze and compare the latest developments in this fast growing field of applied mathematics and to identify topics of research which are of special interest for industrial applications and for further theoretical study. Inherently parallel algorithms, that is, computational methods which are, by their mathematical nature, parallel, have been studied in various contexts for more than fifty years. However, it was only during the last decade that they have mostly proved their practical usefulness because new generations of computers made their implementation possible in order to solve complex feasibility and optimization problems involving huge amounts of data via parallel processing. These led to an accumulation of computational experience and theoretical information and opened new and challenging questions concerning the behavior of inherently parallel algorithms for feasibility and optimization, their convergence in new environments and in circumstances in which they were not considered before their stability and reliability. Several research groups all over the world focused on these questions and it was the general feeling among scientists involved in this effort that the time has come to survey the latest progress and convey a perspective for further development and concerted scientific investigations. Thus, the editors of this volume, with the support of the Israeli Academy for Sciences and Humanities, took the initiative of organizing a Workshop intended to bring together the leading scientists in the field. The current volume is the Proceedings of the Workshop representing the discussions, debates and communications that took place. Having all that information collected in a single book will provide mathematicians and engineers interested in the theoretical and practical aspects of the inherently parallel algorithms for feasibility and optimization with a tool for determining when, where and which algorithms in this class are fit for solving specific problems, how reliable they are, how they behave and how efficient they were in previous applications. Such a tool will allow software creators to choose ways of better implementing these methods by learning from existing experience.

Mathematical Analysis and Applications

Mathematical Analysis and Applications

Author: Themistocles M. Rassias

Publisher: Springer Nature

Published: 2019-12-12

Total Pages: 694

ISBN-13: 3030313395

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An international community of experts scientists comprise the research and survey contributions in this volume which covers a broad spectrum of areas in which analysis plays a central role. Contributions discuss theory and problems in real and complex analysis, functional analysis, approximation theory, operator theory, analytic inequalities, the Radon transform, nonlinear analysis, and various applications of interdisciplinary research; some are also devoted to specific applications such as the three-body problem, finite element analysis in fluid mechanics, algorithms for difference of monotone operators, a vibrational approach to a financial problem, and more. This volume is useful to graduate students and researchers working in mathematics, physics, engineering, and economics.


Book Synopsis Mathematical Analysis and Applications by : Themistocles M. Rassias

Download or read book Mathematical Analysis and Applications written by Themistocles M. Rassias and published by Springer Nature. This book was released on 2019-12-12 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: An international community of experts scientists comprise the research and survey contributions in this volume which covers a broad spectrum of areas in which analysis plays a central role. Contributions discuss theory and problems in real and complex analysis, functional analysis, approximation theory, operator theory, analytic inequalities, the Radon transform, nonlinear analysis, and various applications of interdisciplinary research; some are also devoted to specific applications such as the three-body problem, finite element analysis in fluid mechanics, algorithms for difference of monotone operators, a vibrational approach to a financial problem, and more. This volume is useful to graduate students and researchers working in mathematics, physics, engineering, and economics.

Federated Learning Techniques And Its Application In The Healthcare Industry

Federated Learning Techniques And Its Application In The Healthcare Industry

Author: H L Gururaj

Publisher: World Scientific

Published: 2024-05-28

Total Pages: 235

ISBN-13: 9811287953

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Federated Learning is currently an emerging technology in the field of machine learning. Federated Learning is a structure which trains a centralized model for a given assignment, where the data is de-centralized across different edge devices or servers. This enables preservation of the confidentiality of data on various edge devices, as only the updated outcomes of the models are shared with the centralized model. This means the data can remain on each edge device, while we can still train a model using that data.Federated Learning has greatly increased the potential to transmute data in the healthcare industry, enabling healthcare professionals to improve treatment of patients.This book comprises chapters on applying Federated models in the field of healthcare industry.Federated Learning mainly concentrates on securing the privacy of data by training local data in a shared global model without putting the training data in a centralized location. The importance of federated learning lies in its innumerable uses in health care that ranges from maintaining the privacy of raw data of the patients, discover clinically alike patients, forecasting hospitalization due to cardiac events impermanence and probable solutions to the same. The goal of this edited book is to provide a reference guide to the theme.


Book Synopsis Federated Learning Techniques And Its Application In The Healthcare Industry by : H L Gururaj

Download or read book Federated Learning Techniques And Its Application In The Healthcare Industry written by H L Gururaj and published by World Scientific. This book was released on 2024-05-28 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: Federated Learning is currently an emerging technology in the field of machine learning. Federated Learning is a structure which trains a centralized model for a given assignment, where the data is de-centralized across different edge devices or servers. This enables preservation of the confidentiality of data on various edge devices, as only the updated outcomes of the models are shared with the centralized model. This means the data can remain on each edge device, while we can still train a model using that data.Federated Learning has greatly increased the potential to transmute data in the healthcare industry, enabling healthcare professionals to improve treatment of patients.This book comprises chapters on applying Federated models in the field of healthcare industry.Federated Learning mainly concentrates on securing the privacy of data by training local data in a shared global model without putting the training data in a centralized location. The importance of federated learning lies in its innumerable uses in health care that ranges from maintaining the privacy of raw data of the patients, discover clinically alike patients, forecasting hospitalization due to cardiac events impermanence and probable solutions to the same. The goal of this edited book is to provide a reference guide to the theme.

Artificial Intelligence and Its Applications

Artificial Intelligence and Its Applications

Author: Brahim Lejdel

Publisher: Springer Nature

Published: 2022-03-11

Total Pages: 613

ISBN-13: 303096311X

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This book contains the proceedings of the second edition of the international Conference on Artificial Intelligence and its Applications (AIAP'21). This edition aims to bring together leading academic scientists, international researchers, and practitioners to exchange and share their experiences and research results on all aspects of Artificial Intelligence. It also provides an interdisciplinary platform for researchers, practitioners and students to present and discuss the most recent innovations, trends, and concerns as well as practical challenges encountered and solutions adopted in the fields of Artificial Intelligence. This international conference offers an opportunity to bridge the gap between the Artificial Intelligence research community and people from the industry or working in other research areas including smart cities, big data, cloud computing, social networks, and energy.


Book Synopsis Artificial Intelligence and Its Applications by : Brahim Lejdel

Download or read book Artificial Intelligence and Its Applications written by Brahim Lejdel and published by Springer Nature. This book was released on 2022-03-11 with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the second edition of the international Conference on Artificial Intelligence and its Applications (AIAP'21). This edition aims to bring together leading academic scientists, international researchers, and practitioners to exchange and share their experiences and research results on all aspects of Artificial Intelligence. It also provides an interdisciplinary platform for researchers, practitioners and students to present and discuss the most recent innovations, trends, and concerns as well as practical challenges encountered and solutions adopted in the fields of Artificial Intelligence. This international conference offers an opportunity to bridge the gap between the Artificial Intelligence research community and people from the industry or working in other research areas including smart cities, big data, cloud computing, social networks, and energy.