Methods For Large Scale Convex Optimization Problems With L1 Regularization
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Methods For Large Scale Convex Optimization Problems With L1 Regularization
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Author : Kwangmoo Koh
language : en
Publisher:
Release Date : 2008
Methods For Large Scale Convex Optimization Problems With L1 Regularization written by Kwangmoo Koh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.
Much of recent research in signal processing, statistics, and many other fields has focused on ℓ1 regularization based methods for feature selection, sparse signal reconstruction. In this thesis we study optimization problems with ℓ1 regularization, and efficient methods to solve them.
Convex Optimization In Signal Processing And Communications
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Author : Daniel P. Palomar
language : en
Publisher: Cambridge University Press
Release Date : 2010
Convex Optimization In Signal Processing And Communications written by Daniel P. Palomar and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Computers categories.
Leading experts provide the theoretical underpinnings of the subject plus tutorials on a wide range of applications, from automatic code generation to robust broadband beamforming. Emphasis on cutting-edge research and formulating problems in convex form make this an ideal textbook for advanced graduate courses and a useful self-study guide.
Mathematical Methods In Engineering
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Author : Kenan Taş
language : en
Publisher: Springer
Release Date : 2018-08-02
Mathematical Methods In Engineering written by Kenan Taş and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-02 with Technology & Engineering categories.
This book presents recent developments in nonlinear dynamics with an emphasis on complex systems. The volume illustrates new methods to characterize the solutions of nonlinear dynamics associated with complex systems. This book contains the following topics: new solutions of the functional equations, optimization algorithm for traveling salesman problem, fractals, control, fractional calculus models, fractional discretization, local fractional partial differential equations and their applications, and solutions of fractional kinetic equations.
Regularization Optimization Kernels And Support Vector Machines
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Author : Johan A.K. Suykens
language : en
Publisher: CRC Press
Release Date : 2014-10-23
Regularization Optimization Kernels And Support Vector Machines written by Johan A.K. Suykens and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-23 with Computers categories.
Regularization, Optimization, Kernels, and Support Vector Machines offers a snapshot of the current state of the art of large-scale machine learning, providing a single multidisciplinary source for the latest research and advances in regularization, sparsity, compressed sensing, convex and large-scale optimization, kernel methods, and support vecto
Large Scale Inverse Problems
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Author : Mike Cullen
language : en
Publisher: Walter de Gruyter
Release Date : 2013-08-29
Large Scale Inverse Problems written by Mike Cullen and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-29 with Mathematics categories.
This book is thesecond volume of a three volume series recording the "Radon Special Semester 2011 on Multiscale Simulation & Analysis in Energy and the Environment" that took placein Linz, Austria, October 3-7, 2011. This volume addresses the common ground in the mathematical and computational procedures required for large-scale inverse problems and data assimilation in forefront applications. The solution of inverse problems is fundamental to a wide variety of applications such as weather forecasting, medical tomography, and oil exploration. Regularisation techniques are needed to ensure solutions of sufficient quality to be useful, and soundly theoretically based. This book addresses the common techniques required for all the applications, and is thus truly interdisciplinary. Thiscollection of surveyarticlesfocusses onthe large inverse problems commonly arising in simulation and forecasting in the earth sciences. For example, operational weather forecasting models have between 107 and 108 degrees of freedom. Even so, these degrees of freedom represent grossly space-time averaged properties of the atmosphere. Accurate forecasts require accurate initial conditions. With recent developments in satellite data, there are between 106 and 107 observations each day. However, while these also represent space-time averaged properties, the averaging implicit in the measurements is quite different from that used in the models. In atmosphere and ocean applications, there is a physically-based model available which can be used to regularise the problem. We assume that there is a set of observations with known error characteristics available over a period of time. The basic deterministic technique is to fit a model trajectory to the observations over a period of time to within the observation error. Since the model is not perfect the model trajectory has to be corrected, which defines the data assimilation problem. The stochastic view can be expressed by using an ensemble of model trajectories, and calculating corrections to both the mean value and the spread which allow the observations to be fitted by each ensemble member. In other areas of earth science, only the structure of the model formulation itself is known and the aim is to use the past observation history to determine the unknown model parameters. The book records the achievements of Workshop2 "Large-Scale Inverse Problems and Applications in the Earth Sciences". Itinvolves experts in the theory of inverse problems together with experts working on both theoretical and practical aspects of the techniques by which large inverse problems arise in the earth sciences.
Convex Optimization
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Author : Stephen P. Boyd
language : en
Publisher: Cambridge University Press
Release Date : 2004-03-08
Convex Optimization written by Stephen P. Boyd and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-08 with Business & Economics categories.
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.
Optimization In Machine Learning And Applications
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Author : Anand J. Kulkarni
language : en
Publisher: Springer
Release Date : 2020-12-10
Optimization In Machine Learning And Applications written by Anand J. Kulkarni and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-10 with Technology & Engineering categories.
This book discusses one of the major applications of artificial intelligence: the use of machine learning to extract useful information from multimodal data. It discusses the optimization methods that help minimize the error in developing patterns and classifications, which further helps improve prediction and decision-making. The book also presents formulations of real-world machine learning problems, and discusses AI solution methodologies as standalone or hybrid approaches. Lastly, it proposes novel metaheuristic methods to solve complex machine learning problems. Featuring valuable insights, the book helps readers explore new avenues leading toward multidisciplinary research discussions.
Study On Signal Detection And Recovery Methods With Joint Sparsity
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Author : Xueqian Wang
language : en
Publisher: Springer Nature
Release Date : 2023-09-30
Study On Signal Detection And Recovery Methods With Joint Sparsity written by Xueqian Wang and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-30 with Technology & Engineering categories.
The task of signal detection is deciding whether signals of interest exist by using their observed data. Furthermore, signals are reconstructed or their key parameters are estimated from the observations in the task of signal recovery. Sparsity is a natural characteristic of most of signals in practice. The fact that multiple sparse signals share the common locations of dominant coefficients is called by joint sparsity. In the context of signal processing, joint sparsity model results in higher performance of signal detection and recovery. This book focuses on the task of detecting and reconstructing signals with joint sparsity. The main contents include key methods for detection of joint sparse signals and their corresponding theoretical performance analysis, and methods for joint sparse signal recovery and their application in the context of radar imaging.
Stochastic Optimization For Large Scale Machine Learning
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Author : Vinod Kumar Chauhan
language : en
Publisher: CRC Press
Release Date : 2021-11-18
Stochastic Optimization For Large Scale Machine Learning written by Vinod Kumar Chauhan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-18 with Computers categories.
Advancements in the technology and availability of data sources have led to the `Big Data' era. Working with large data offers the potential to uncover more fine-grained patterns and take timely and accurate decisions, but it also creates a lot of challenges such as slow training and scalability of machine learning models. One of the major challenges in machine learning is to develop efficient and scalable learning algorithms, i.e., optimization techniques to solve large scale learning problems. Stochastic Optimization for Large-scale Machine Learning identifies different areas of improvement and recent research directions to tackle the challenge. Developed optimisation techniques are also explored to improve machine learning algorithms based on data access and on first and second order optimisation methods. Key Features: Bridges machine learning and Optimisation. Bridges theory and practice in machine learning. Identifies key research areas and recent research directions to solve large-scale machine learning problems. Develops optimisation techniques to improve machine learning algorithms for big data problems. The book will be a valuable reference to practitioners and researchers as well as students in the field of machine learning.
Handbook Of Variational Methods For Nonlinear Geometric Data
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Author : Philipp Grohs
language : en
Publisher: Springer Nature
Release Date : 2020-04-03
Handbook Of Variational Methods For Nonlinear Geometric Data written by Philipp Grohs and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-03 with Mathematics categories.
This book covers different, current research directions in the context of variational methods for non-linear geometric data. Each chapter is authored by leading experts in the respective discipline and provides an introduction, an overview and a description of the current state of the art. Non-linear geometric data arises in various applications in science and engineering. Examples of nonlinear data spaces are diverse and include, for instance, nonlinear spaces of matrices, spaces of curves, shapes as well as manifolds of probability measures. Applications can be found in biology, medicine, product engineering, geography and computer vision for instance. Variational methods on the other hand have evolved to being amongst the most powerful tools for applied mathematics. They involve techniques from various branches of mathematics such as statistics, modeling, optimization, numerical mathematics and analysis. The vast majority of research on variational methods, however, is focused on data in linear spaces. Variational methods for non-linear data is currently an emerging research topic. As a result, and since such methods involve various branches of mathematics, there is a plethora of different, recent approaches dealing with different aspects of variational methods for nonlinear geometric data. Research results are rather scattered and appear in journals of different mathematical communities. The main purpose of the book is to account for that by providing, for the first time, a comprehensive collection of different research directions and existing approaches in this context. It is organized in a way that leading researchers from the different fields provide an introductory overview of recent research directions in their respective discipline. As such, the book is a unique reference work for both newcomers in the field of variational methods for non-linear geometric data, as well as for established experts that aim at to exploit new research directions or collaborations. Chapter 9 of this book is available open access under a CC BY 4.0 license at link.springer.com.