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Author: Jagdish S. Rustagi
Publisher: Elsevier
ISBN: 1483295710
Category : Mathematics
Languages : en
Pages : 376
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Book Description
Statistics help guide us to optimal decisions under uncertainty. A large variety of statistical problems are essentially solutions to optimization problems. The mathematical techniques of optimization are fundamentalto statistical theory and practice. In this book, Jagdish Rustagi provides full-spectrum coverage of these methods, ranging from classical optimization and Lagrange multipliers, to numerical techniques using gradients or direct search, to linear, nonlinear, and dynamic programming using the Kuhn-Tucker conditions or the Pontryagin maximal principle. Variational methods and optimization in function spaces are also discussed, as are stochastic optimization in simulation, including annealing methods. The text features numerous applications, including: Finding maximum likelihood estimates, Markov decision processes, Programming methods used to optimize monitoring of patients in hospitals, Derivation of the Neyman-Pearson lemma, The search for optimal designs, Simulation of a steel mill. Suitable as both a reference and a text, this book will be of interest to advanced undergraduate or beginning graduate students in statistics, operations research, management and engineering sciences, and related fields. Most of the material can be covered in one semester by students with a basic background in probability and statistics. - Covers optimization from traditional methods to recent developments such as Karmarkars algorithm and simulated annealing - Develops a wide range of statistical techniques in the unified context of optimization - Discusses applications such as optimizing monitoring of patients and simulating steel mill operations - Treats numerical methods and applications - Includes exercises and references for each chapter - Covers topics such as linear, nonlinear, and dynamic programming, variational methods, and stochastic optimization
Author: Jagdish S. Rustagi
Publisher: Elsevier
ISBN: 1483295710
Category : Mathematics
Languages : en
Pages : 376
Get Book Here
Book Description
Statistics help guide us to optimal decisions under uncertainty. A large variety of statistical problems are essentially solutions to optimization problems. The mathematical techniques of optimization are fundamentalto statistical theory and practice. In this book, Jagdish Rustagi provides full-spectrum coverage of these methods, ranging from classical optimization and Lagrange multipliers, to numerical techniques using gradients or direct search, to linear, nonlinear, and dynamic programming using the Kuhn-Tucker conditions or the Pontryagin maximal principle. Variational methods and optimization in function spaces are also discussed, as are stochastic optimization in simulation, including annealing methods. The text features numerous applications, including: Finding maximum likelihood estimates, Markov decision processes, Programming methods used to optimize monitoring of patients in hospitals, Derivation of the Neyman-Pearson lemma, The search for optimal designs, Simulation of a steel mill. Suitable as both a reference and a text, this book will be of interest to advanced undergraduate or beginning graduate students in statistics, operations research, management and engineering sciences, and related fields. Most of the material can be covered in one semester by students with a basic background in probability and statistics. - Covers optimization from traditional methods to recent developments such as Karmarkars algorithm and simulated annealing - Develops a wide range of statistical techniques in the unified context of optimization - Discusses applications such as optimizing monitoring of patients and simulating steel mill operations - Treats numerical methods and applications - Includes exercises and references for each chapter - Covers topics such as linear, nonlinear, and dynamic programming, variational methods, and stochastic optimization
Author: B. Everitt
Publisher: Springer Science & Business Media
ISBN: 9400931530
Category : Science
Languages : en
Pages : 87
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Book Description
Optimization techniques are used to find the values of a set of parameters which maximize or minimize some objective function of interest. Such methods have become of great importance in statistics for estimation, model fitting, etc. This text attempts to give a brief introduction to optimization methods and their use in several important areas of statistics. It does not pretend to provide either a complete treatment of optimization techniques or a comprehensive review of their application in statistics; such a review would, of course, require a volume several orders of magnitude larger than this since almost every issue of every statistics journal contains one or other paper which involves the application of an optimization method. It is hoped that the text will be useful to students on applied statistics courses and to researchers needing to use optimization techniques in a statistical context. Lastly, my thanks are due to Bertha Lakey for typing the manuscript.
Author: Stephen J. Wright
Publisher: Cambridge University Press
ISBN: 1316518981
Category : Computers
Languages : en
Pages : 239
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Book Description
A concise text that presents and analyzes the fundamental techniques and methods in optimization that are useful in data science.
Author: Xin-She Yang
Publisher: John Wiley & Sons
ISBN: 1119490545
Category : Mathematics
Languages : en
Pages : 384
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Book Description
A guide to modern optimization applications and techniques in newly emerging areas spanning optimization, data science, machine intelligence, engineering, and computer sciences Optimization Techniques and Applications with Examples introduces the fundamentals of all the commonly used techniques in optimization that encompass the broadness and diversity of the methods (traditional and new) and algorithms. The author—a noted expert in the field—covers a wide range of topics including mathematical foundations, optimization formulation, optimality conditions, algorithmic complexity, linear programming, convex optimization, and integer programming. In addition, the book discusses artificial neural network, clustering and classifications, constraint-handling, queueing theory, support vector machine and multi-objective optimization, evolutionary computation, nature-inspired algorithms and many other topics. Designed as a practical resource, all topics are explained in detail with step-by-step examples to show how each method works. The book’s exercises test the acquired knowledge that can be potentially applied to real problem solving. By taking an informal approach to the subject, the author helps readers to rapidly acquire the basic knowledge in optimization, operational research, and applied data mining. This important resource: Offers an accessible and state-of-the-art introduction to the main optimization techniques Contains both traditional optimization techniques and the most current algorithms and swarm intelligence-based techniques Presents a balance of theory, algorithms, and implementation Includes more than 100 worked examples with step-by-step explanations Written for upper undergraduates and graduates in a standard course on optimization, operations research and data mining, Optimization Techniques and Applications with Examples is a highly accessible guide to understanding the fundamentals of all the commonly used techniques in optimization.
Author: Ashish Srivastava
Publisher: Springer Science & Business Media
ISBN: 0387265287
Category : Technology & Engineering
Languages : en
Pages : 284
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Book Description
Covers the statistical analysis and optimization issues arising due to increased process variations in current technologies. Comprises a valuable reference for statistical analysis and optimization techniques in current and future VLSI design for CAD-Tool developers and for researchers interested in starting work in this very active area of research. Written by author who lead much research in this area who provide novel ideas and approaches to handle the addressed issues
Author: Anatoli Juditsky
Publisher: Princeton University Press
ISBN: 0691197296
Category : Mathematics
Languages : en
Pages : 655
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Book Description
This authoritative book draws on the latest research to explore the interplay of high-dimensional statistics with optimization. Through an accessible analysis of fundamental problems of hypothesis testing and signal recovery, Anatoli Juditsky and Arkadi Nemirovski show how convex optimization theory can be used to devise and analyze near-optimal statistical inferences. Statistical Inference via Convex Optimization is an essential resource for optimization specialists who are new to statistics and its applications, and for data scientists who want to improve their optimization methods. Juditsky and Nemirovski provide the first systematic treatment of the statistical techniques that have arisen from advances in the theory of optimization. They focus on four well-known statistical problems—sparse recovery, hypothesis testing, and recovery from indirect observations of both signals and functions of signals—demonstrating how they can be solved more efficiently as convex optimization problems. The emphasis throughout is on achieving the best possible statistical performance. The construction of inference routines and the quantification of their statistical performance are given by efficient computation rather than by analytical derivation typical of more conventional statistical approaches. In addition to being computation-friendly, the methods described in this book enable practitioners to handle numerous situations too difficult for closed analytical form analysis, such as composite hypothesis testing and signal recovery in inverse problems. Statistical Inference via Convex Optimization features exercises with solutions along with extensive appendixes, making it ideal for use as a graduate text.
Author: Kenneth Lange
Publisher: Springer Science & Business Media
ISBN: 9780387203324
Category : Business & Economics
Languages : en
Pages : 282
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Book Description
Lange is a Springer author of other successful books. This is the first book that emphasizes the applications of optimization to statistics. The emphasis on statistical applications will be especially appealing to graduate students of statistics and biostatistics.
Author: P. Adby
Publisher: Springer Science & Business Media
ISBN: 940095705X
Category : Science
Languages : en
Pages : 214
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Book Description
During the last decade the techniques of non-linear optim ization have emerged as an important subject for study and research. The increasingly widespread application of optim ization has been stimulated by the availability of digital computers, and the necessity of using them in the investigation of large systems. This book is an introduction to non-linear methods of optimization and is suitable for undergraduate and post graduate courses in mathematics, the physical and social sciences, and engineering. The first half of the book covers the basic optimization techniques including linear search methods, steepest descent, least squares, and the Newton-Raphson method. These are described in detail, with worked numerical examples, since they form the basis from which advanced methods are derived. Since 1965 advanced methods of unconstrained and constrained optimization have been developed to utilise the computational power of the digital computer. The second half of the book describes fully important algorithms in current use such as variable metric methods for unconstrained problems and penalty function methods for constrained problems. Recent work, much of which has not yet been widely applied, is reviewed and compared with currently popular techniques under a few generic main headings. vi PREFACE Chapter I describes the optimization problem in mathemat ical form and defines the terminology used in the remainder of the book. Chapter 2 is concerned with single variable optimization. The main algorithms of both search and approximation methods are developed in detail since they are an essential part of many multi-variable methods.
Author: Enrique del Castillo
Publisher: Springer Science & Business Media
ISBN: 0387714359
Category : Mathematics
Languages : en
Pages : 462
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Book Description
This book covers several bases at once. It is useful as a textbook for a second course in experimental optimization techniques for industrial production processes. In addition, it is a superb reference volume for use by professors and graduate students in Industrial Engineering and Statistics departments. It will also be of huge interest to applied statisticians, process engineers, and quality engineers working in the electronics and biotech manufacturing industries. In all, it provides an in-depth presentation of the statistical issues that arise in optimization problems, including confidence regions on the optimal settings of a process, stopping rules in experimental optimization, and more.
Author: Soliman Abdel-Hady Soliman
Publisher: Springer Science & Business Media
ISBN: 146141752X
Category : Mathematics
Languages : en
Pages : 430
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Book Description
This book presents the application of some AI related optimization techniques in the operation and control of electric power systems. With practical applications and examples the use of functional analysis, simulated annealing, Tabu-search, Genetic algorithms and fuzzy systems for the optimization of power systems is discussed in detail. Preliminary mathematical concepts are presented before moving to more advanced material. Researchers and graduate students will benefit from this book. Engineers working in utility companies, operations and control, and resource management will also find this book useful.
