First Order Methods In Optimization
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First Order Methods In Optimization
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Author : Amir Beck
language : en
Publisher: SIAM
Release Date : 2017-10-02
First Order Methods In Optimization written by Amir Beck and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-02 with Mathematics categories.
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.
First Order And Stochastic Optimization Methods For Machine Learning
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Author : Guanghui Lan
language : en
Publisher: Springer Nature
Release Date : 2020-05-15
First Order And Stochastic Optimization Methods For Machine Learning written by Guanghui Lan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-15 with Mathematics categories.
This book covers not only foundational materials but also the most recent progresses made during the past few years on the area of machine learning algorithms. In spite of the intensive research and development in this area, there does not exist a systematic treatment to introduce the fundamental concepts and recent progresses on machine learning algorithms, especially on those based on stochastic optimization methods, randomized algorithms, nonconvex optimization, distributed and online learning, and projection free methods. This book will benefit the broad audience in the area of machine learning, artificial intelligence and mathematical programming community by presenting these recent developments in a tutorial style, starting from the basic building blocks to the most carefully designed and complicated algorithms for machine learning.
Accelerated Optimization For Machine Learning
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Author : Zhouchen Lin
language : en
Publisher: Springer Nature
Release Date : 2020-05-29
Accelerated Optimization For Machine Learning written by Zhouchen Lin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-29 with Computers categories.
This book on optimization includes forewords by Michael I. Jordan, Zongben Xu and Zhi-Quan Luo. Machine learning relies heavily on optimization to solve problems with its learning models, and first-order optimization algorithms are the mainstream approaches. The acceleration of first-order optimization algorithms is crucial for the efficiency of machine learning. Written by leading experts in the field, this book provides a comprehensive introduction to, and state-of-the-art review of accelerated first-order optimization algorithms for machine learning. It discusses a variety of methods, including deterministic and stochastic algorithms, where the algorithms can be synchronous or asynchronous, for unconstrained and constrained problems, which can be convex or non-convex. Offering a rich blend of ideas, theories and proofs, the book is up-to-date and self-contained. It is an excellent reference resource for users who are seeking faster optimization algorithms, as well as for graduate students and researchers wanting to grasp the frontiers of optimization in machine learning in a short time.
Introduction To Nonlinear Optimization
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Author : Amir Beck
language : en
Publisher: SIAM
Release Date : 2014-10-27
Introduction To Nonlinear Optimization written by Amir Beck and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-27 with Mathematics categories.
This book provides the foundations of the theory of nonlinear optimization as well as some related algorithms and presents a variety of applications from diverse areas of applied sciences. The author combines three pillars of optimization?theoretical and algorithmic foundation, familiarity with various applications, and the ability to apply the theory and algorithms on actual problems?and rigorously and gradually builds the connection between theory, algorithms, applications, and implementation. Readers will find more than 170 theoretical, algorithmic, and numerical exercises that deepen and enhance the reader's understanding of the topics. The author includes offers several subjects not typically found in optimization books?for example, optimality conditions in sparsity-constrained optimization, hidden convexity, and total least squares. The book also offers a large number of applications discussed theoretically and algorithmically, such as circle fitting, Chebyshev center, the Fermat?Weber problem, denoising, clustering, total least squares, and orthogonal regression and theoretical and algorithmic topics demonstrated by the MATLAB? toolbox CVX and a package of m-files that is posted on the book?s web site.
Stochastic Optimization Methods
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Author : Kurt Marti
language : en
Publisher: Springer
Release Date : 2015-02-21
Stochastic Optimization Methods written by Kurt Marti and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-21 with Business & Economics categories.
This book examines optimization problems that in practice involve random model parameters. It details the computation of robust optimal solutions, i.e., optimal solutions that are insensitive with respect to random parameter variations, where appropriate deterministic substitute problems are needed. Based on the probability distribution of the random data and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into appropriate deterministic substitute problems. Due to the probabilities and expectations involved, the book also shows how to apply approximative solution techniques. Several deterministic and stochastic approximation methods are provided: Taylor expansion methods, regression and response surface methods (RSM), probability inequalities, multiple linearization of survival/failure domains, discretization methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation and gradient procedures and differentiation formulas for probabilities and expectations. In the third edition, this book further develops stochastic optimization methods. In particular, it now shows how to apply stochastic optimization methods to the approximate solution of important concrete problems arising in engineering, economics and operations research.
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 For Data Analysis
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Author : Stephen J. Wright
language : en
Publisher: Cambridge University Press
Release Date : 2022-04-21
Optimization For Data Analysis written by Stephen J. Wright 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 2022-04-21 with Computers categories.
A concise text that presents and analyzes the fundamental techniques and methods in optimization that are useful in data science.
Lectures On Convex Optimization
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Author : Yurii Nesterov
language : en
Publisher: Springer
Release Date : 2018-11-19
Lectures On Convex Optimization written by Yurii Nesterov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-19 with Mathematics categories.
This book provides a comprehensive, modern introduction to convex optimization, a field that is becoming increasingly important in applied mathematics, economics and finance, engineering, and computer science, notably in data science and machine learning. Written by a leading expert in the field, this book includes recent advances in the algorithmic theory of convex optimization, naturally complementing the existing literature. It contains a unified and rigorous presentation of the acceleration techniques for minimization schemes of first- and second-order. It provides readers with a full treatment of the smoothing technique, which has tremendously extended the abilities of gradient-type methods. Several powerful approaches in structural optimization, including optimization in relative scale and polynomial-time interior-point methods, are also discussed in detail. Researchers in theoretical optimization as well as professionals working on optimization problems will find this book very useful. It presents many successful examples of how to develop very fast specialized minimization algorithms. Based on the author’s lectures, it can naturally serve as the basis for introductory and advanced courses in convex optimization for students in engineering, economics, computer science and mathematics.
Fundamentals Of Optimization Techniques With Algorithms
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Author : Sukanta Nayak
language : en
Publisher: Academic Press
Release Date : 2020-08-25
Fundamentals Of Optimization Techniques With Algorithms written by Sukanta Nayak and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-25 with Technology & Engineering categories.
Optimization is a key concept in mathematics, computer science, and operations research, and is essential to the modeling of any system, playing an integral role in computer-aided design. Fundamentals of Optimization Techniques with Algorithms presents a complete package of various traditional and advanced optimization techniques along with a variety of example problems, algorithms and MATLAB© code optimization techniques, for linear and nonlinear single variable and multivariable models, as well as multi-objective and advanced optimization techniques. It presents both theoretical and numerical perspectives in a clear and approachable way. In order to help the reader apply optimization techniques in practice, the book details program codes and computer-aided designs in relation to real-world problems. Ten chapters cover, an introduction to optimization; linear programming; single variable nonlinear optimization; multivariable unconstrained nonlinear optimization; multivariable constrained nonlinear optimization; geometric programming; dynamic programming; integer programming; multi-objective optimization; and nature-inspired optimization. This book provides accessible coverage of optimization techniques, and helps the reader to apply them in practice. Presents optimization techniques clearly, including worked-out examples, from traditional to advanced Maps out the relations between optimization and other mathematical topics and disciplines Provides systematic coverage of algorithms to facilitate computer coding Gives MATLAB© codes in relation to optimization techniques and their use in computer-aided design Presents nature-inspired optimization techniques including genetic algorithms and artificial neural networks
Optimization For Machine Learning
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Author : Suvrit Sra
language : en
Publisher: MIT Press
Release Date : 2012
Optimization For Machine Learning written by Suvrit Sra and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Computers categories.
An up-to-date account of the interplay between optimization and machine learning, accessible to students and researchers in both communities. The interplay between optimization and machine learning is one of the most important developments in modern computational science. Optimization formulations and methods are proving to be vital in designing algorithms to extract essential knowledge from huge volumes of data. Machine learning, however, is not simply a consumer of optimization technology but a rapidly evolving field that is itself generating new optimization ideas. This book captures the state of the art of the interaction between optimization and machine learning in a way that is accessible to researchers in both fields. Optimization approaches have enjoyed prominence in machine learning because of their wide applicability and attractive theoretical properties. The increasing complexity, size, and variety of today's machine learning models call for the reassessment of existing assumptions. This book starts the process of reassessment. It describes the resurgence in novel contexts of established frameworks such as first-order methods, stochastic approximations, convex relaxations, interior-point methods, and proximal methods. It also devotes attention to newer themes such as regularized optimization, robust optimization, gradient and subgradient methods, splitting techniques, and second-order methods. Many of these techniques draw inspiration from other fields, including operations research, theoretical computer science, and subfields of optimization. The book will enrich the ongoing cross-fertilization between the machine learning community and these other fields, and within the broader optimization community.