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Author : Tobias Lindstrøm Jensen
Publisher :
Page : pages
File Size : 27,80 MB
Release : 2011
Category :
ISBN : 9788792328762
Author : Vishal Monga
Publisher : Springer
Page : 238 pages
File Size : 16,7 MB
Release : 2017-10-27
Category : Computers
ISBN : 3319616099
This book covers recent advances in image processing and imaging sciences from an optimization viewpoint, especially convex optimization with the goal of designing tractable algorithms. Throughout the handbook, the authors introduce topics on the most key aspects of image acquisition and processing that are based on the formulation and solution of novel optimization problems. The first part includes a review of the mathematical methods and foundations required, and covers topics in image quality optimization and assessment. The second part of the book discusses concepts in image formation and capture from color imaging to radar and multispectral imaging. The third part focuses on sparsity constrained optimization in image processing and vision and includes inverse problems such as image restoration and de-noising, image classification and recognition and learning-based problems pertinent to image understanding. Throughout, convex optimization techniques are shown to be a critically important mathematical tool for imaging science problems and applied extensively. Convex Optimization Methods in Imaging Science is the first book of its kind and will appeal to undergraduate and graduate students, industrial researchers and engineers and those generally interested in computational aspects of modern, real-world imaging and image processing problems.
Author : Amir Beck
Publisher : SIAM
Page : 476 pages
File Size : 47,38 MB
Release : 2017-10-02
Category : Mathematics
ISBN : 1611974984
The primary goal of this book is to provide a self-contained, comprehensive study of the main ?rst-order methods that are frequently used in solving large-scale problems. First-order methods exploit information on values and gradients/subgradients (but not Hessians) of the functions composing the model under consideration. With the increase in the number of applications that can be modeled as large or even huge-scale optimization problems, there has been a revived interest in using simple methods that require low iteration cost as well as low memory storage. The author has gathered, reorganized, and synthesized (in a unified manner) many results that are currently scattered throughout the literature, many of which cannot be typically found in optimization books. First-Order Methods in Optimization offers comprehensive study of first-order methods with the theoretical foundations; provides plentiful examples and illustrations; emphasizes rates of convergence and complexity analysis of the main first-order methods used to solve large-scale problems; and covers both variables and functional decomposition methods.
Author : Ernest K. Ryu
Publisher : Cambridge University Press
Page : 320 pages
File Size : 33,22 MB
Release : 2022-12-01
Category : Mathematics
ISBN : 1009191063
Starting from where a first course in convex optimization leaves off, this text presents a unified analysis of first-order optimization methods – including parallel-distributed algorithms – through the abstraction of monotone operators. With the increased computational power and availability of big data over the past decade, applied disciplines have demanded that larger and larger optimization problems be solved. This text covers the first-order convex optimization methods that are uniquely effective at solving these large-scale optimization problems. Readers will have the opportunity to construct and analyze many well-known classical and modern algorithms using monotone operators, and walk away with a solid understanding of the diverse optimization algorithms. Graduate students and researchers in mathematical optimization, operations research, electrical engineering, statistics, and computer science will appreciate this concise introduction to the theory of convex optimization algorithms.
Author : Yuyuan Ouyang
Publisher :
Page : 190 pages
File Size : 24,7 MB
Release : 2013
Category :
ISBN :
This PhD Dissertation concerns optimal first order methods in convex optimization, and their applications in imaging science. The research is motivated by the rapid advances in the technologies for digital data acquisition, which results in high demand for efficient algorithms to solve non-smooth convex optimization problems. In this dissertation we will develop theories and optimal numerical methods for solving a class of deterministic and stochastic saddle point problems and more general variational inequalities arising from large-scale data analysis problems. In the first part of this dissertation, we aim to solve a class of deterministic and stochastic saddle point problems (SPP), which has been considered as a framework of ill-posed inverse problems regularized by a non-smooth functional in many data analysis problems, such as image reconstruction in compressed sensing and machine learning. The proposed deterministic accelerated primal dual (APD) algorithm is expected to have the same optimal rate of convergence as the one obtained by Nesterov for a different scheme. We also propose a stochastic APD algorithm that also exhibits an optimal rate of convergence. To our best knowledge, no stochastic primal-dual algorithms have been developed in literatures.
Author : Chong-Yung Chi
Publisher : CRC Press
Page : 456 pages
File Size : 39,31 MB
Release : 2017-01-24
Category : Technology & Engineering
ISBN : 1498776469
Convex Optimization for Signal Processing and Communications: From Fundamentals to Applications provides fundamental background knowledge of convex optimization, while striking a balance between mathematical theory and applications in signal processing and communications. In addition to comprehensive proofs and perspective interpretations for core convex optimization theory, this book also provides many insightful figures, remarks, illustrative examples, and guided journeys from theory to cutting-edge research explorations, for efficient and in-depth learning, especially for engineering students and professionals. With the powerful convex optimization theory and tools, this book provides you with a new degree of freedom and the capability of solving challenging real-world scientific and engineering problems.
Author : Sébastien Bubeck
Publisher : Foundations and Trends (R) in Machine Learning
Page : 142 pages
File Size : 46,90 MB
Release : 2015-11-12
Category : Convex domains
ISBN : 9781601988607
This monograph presents the main complexity theorems in convex optimization and their corresponding algorithms. It begins with the fundamental theory of black-box optimization and proceeds to guide the reader through recent advances in structural optimization and stochastic optimization. The presentation of black-box optimization, strongly influenced by the seminal book by Nesterov, includes the analysis of cutting plane methods, as well as (accelerated) gradient descent schemes. Special attention is also given to non-Euclidean settings (relevant algorithms include Frank-Wolfe, mirror descent, and dual averaging), and discussing their relevance in machine learning. The text provides a gentle introduction to structural optimization with FISTA (to optimize a sum of a smooth and a simple non-smooth term), saddle-point mirror prox (Nemirovski's alternative to Nesterov's smoothing), and a concise description of interior point methods. In stochastic optimization it discusses stochastic gradient descent, mini-batches, random coordinate descent, and sublinear algorithms. It also briefly touches upon convex relaxation of combinatorial problems and the use of randomness to round solutions, as well as random walks based methods.
Author : Stephen P. Boyd
Publisher : Cambridge University Press
Page : 744 pages
File Size : 45,84 MB
Release : 2004-03-08
Category : Business & Economics
ISBN : 9780521833783
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.
Author : Amir Beck
Publisher : SIAM
Page : 487 pages
File Size : 45,98 MB
Release : 2017-10-02
Category : Mathematics
ISBN : 1611974992
The primary goal of this book is to provide a self-contained, comprehensive study of the main ?rst-order methods that are frequently used in solving large-scale problems. First-order methods exploit information on values and gradients/subgradients (but not Hessians) of the functions composing the model under consideration. With the increase in the number of applications that can be modeled as large or even huge-scale optimization problems, there has been a revived interest in using simple methods that require low iteration cost as well as low memory storage. The author has gathered, reorganized, and synthesized (in a unified manner) many results that are currently scattered throughout the literature, many of which cannot be typically found in optimization books. First-Order Methods in Optimization offers comprehensive study of first-order methods with the theoretical foundations; provides plentiful examples and illustrations; emphasizes rates of convergence and complexity analysis of the main first-order methods used to solve large-scale problems; and covers both variables and functional decomposition methods.
Author : Rong Rong
Publisher :
Page : 95 pages
File Size : 38,88 MB
Release : 2013
Category :
ISBN :
Several important applications in machine learning, data mining, signal and image processing can be formulated as the problem of factoring a large data matrix as a product of sparse matrices. Sparse matrix factorization problems are usually solved via alternating convex optimization methods. These methods involve at each iteration a large convex optimization problem with non-differentiable cost and constraint functions, which is typically solved by block coordinate descent algorithm. In this thesis, we investigate first-order algorithms based on forward-backward splitting and Douglas-Rachford splitting algorithms, as an alternative to the block coordinate descent algorithm. We describe efficient methods to evaluate the proximal operators and resolvents needed in the splitting algorithms. We discuss in detail two applications: Structured Sparse Principal Component Analysis and Sparse Dictionary Learning. For these two applications, we compare the splitting algorithms and block coordinate descent on synthetic data and benchmark data sets. Experimental results show that several of the splitting methods, in particular Tseng's modified forward-backward method and the Chambolle-Pock splitting method, are often faster and more accurate than the block coordinate descent algorithm.