Iterative Methods For Optimization

Author : C. T. Kelley
Publisher : SIAM
Page : 195 pages
File Size : 47,7 Mb
Release : 1999-01-01
Category : Mathematics
ISBN : 161197092X

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Iterative Methods for Optimization by C. T. Kelley Pdf

This book presents a carefully selected group of methods for unconstrained and bound constrained optimization problems and analyzes them in depth both theoretically and algorithmically. It focuses on clarity in algorithmic description and analysis rather than generality, and while it provides pointers to the literature for the most general theoretical results and robust software, the author thinks it is more important that readers have a complete understanding of special cases that convey essential ideas. A companion to Kelley's book, Iterative Methods for Linear and Nonlinear Equations (SIAM, 1995), this book contains many exercises and examples and can be used as a text, a tutorial for self-study, or a reference. Iterative Methods for Optimization does more than cover traditional gradient-based optimization: it is the first book to treat sampling methods, including the Hooke-Jeeves, implicit filtering, MDS, and Nelder-Mead schemes in a unified way, and also the first book to make connections between sampling methods and the traditional gradient-methods. Each of the main algorithms in the text is described in pseudocode, and a collection of MATLAB codes is available. Thus, readers can experiment with the algorithms in an easy way as well as implement them in other languages.

Author : C. T. Kelley
Publisher : SIAM
Page : 184 pages
File Size : 50,9 Mb
Release : 1999-01-01
Category : Mathematics
ISBN : 9780898714333

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Iterative Methods for Optimization by C. T. Kelley Pdf

a carefully selected group of methods for unconstrained and bound constrained optimization problems is analyzed in depth both theoretically and algorithmically. The book focuses on clarity in algorithmic description and analysis rather than generality, and also provides pointers to the literature for the most general theoretical results and robust software,

Author : Lap Chi Lau,R. Ravi,Mohit Singh
Publisher : Cambridge University Press
Page : 255 pages
File Size : 50,8 Mb
Release : 2011-04-18
Category : Computers
ISBN : 9781139499392

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Iterative Methods in Combinatorial Optimization by Lap Chi Lau,R. Ravi,Mohit Singh Pdf

With the advent of approximation algorithms for NP-hard combinatorial optimization problems, several techniques from exact optimization such as the primal-dual method have proven their staying power and versatility. This book describes a simple and powerful method that is iterative in essence and similarly useful in a variety of settings for exact and approximate optimization. The authors highlight the commonality and uses of this method to prove a variety of classical polyhedral results on matchings, trees, matroids and flows. The presentation style is elementary enough to be accessible to anyone with exposure to basic linear algebra and graph theory, making the book suitable for introductory courses in combinatorial optimization at the upper undergraduate and beginning graduate levels. Discussions of advanced applications illustrate their potential for future application in research in approximation algorithms.

Author : C. T. Kelley
Publisher : SIAM
Page : 179 pages
File Size : 40,7 Mb
Release : 1995-01-01
Category : Mathematics
ISBN : 1611970946

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Iterative Methods for Linear and Nonlinear Equations by C. T. Kelley Pdf

Linear and nonlinear systems of equations are the basis for many, if not most, of the models of phenomena in science and engineering, and their efficient numerical solution is critical to progress in these areas. This is the first book to be published on nonlinear equations since the mid-1980s. Although it stresses recent developments in this area, such as Newton-Krylov methods, considerable material on linear equations has been incorporated. This book focuses on a small number of methods and treats them in depth. The author provides a complete analysis of the conjugate gradient and generalized minimum residual iterations as well as recent advances including Newton-Krylov methods, incorporation of inexactness and noise into the analysis, new proofs and implementations of Broyden's method, and globalization of inexact Newton methods. Examples, methods, and algorithmic choices are based on applications to infinite dimensional problems such as partial differential equations and integral equations. The analysis and proof techniques are constructed with the infinite dimensional setting in mind and the computational examples and exercises are based on the MATLAB environment.

Author : Jean-Pierre Corriou
Publisher : Springer Nature
Page : 730 pages
File Size : 53,8 Mb
Release : 2022-01-04
Category : Mathematics
ISBN : 9783030893668

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Numerical Methods and Optimization by Jean-Pierre Corriou Pdf

This text, covering a very large span of numerical methods and optimization, is primarily aimed at advanced undergraduate and graduate students. A background in calculus and linear algebra are the only mathematical requirements. The abundance of advanced methods and practical applications will be attractive to scientists and researchers working in different branches of engineering. The reader is progressively introduced to general numerical methods and optimization algorithms in each chapter. Examples accompany the various methods and guide the students to a better understanding of the applications. The user is often provided with the opportunity to verify their results with complex programming code. Each chapter ends with graduated exercises which furnish the student with new cases to study as well as ideas for exam/homework problems for the instructor. A set of programs made in MatlabTM is available on the author’s personal website and presents both numerical and optimization methods.

Author : Charles Byrne
Publisher : CRC Press
Page : 298 pages
File Size : 47,6 Mb
Release : 2014-02-12
Category : Business & Economics
ISBN : 9781482222340

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Iterative Optimization in Inverse Problems by Charles Byrne Pdf

Iterative Optimization in Inverse Problems brings together a number of important iterative algorithms for medical imaging, optimization, and statistical estimation. It incorporates recent work that has not appeared in other books and draws on the author's considerable research in the field, including his recently developed class of SUMMA algorithms

Author : Yousef Saad
Publisher : SIAM
Page : 537 pages
File Size : 44,9 Mb
Release : 2003-04-01
Category : Mathematics
ISBN : 9780898715347

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Iterative Methods for Sparse Linear Systems by Yousef Saad Pdf

Mathematics of Computing -- General.

Author : J. E. Dennis, Jr.,Robert B. Schnabel
Publisher : SIAM
Page : 394 pages
File Size : 45,8 Mb
Release : 1996-12-01
Category : Mathematics
ISBN : 1611971209

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Numerical Methods for Unconstrained Optimization and Nonlinear Equations by J. E. Dennis, Jr.,Robert B. Schnabel Pdf

This book has become the standard for a complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations. Originally published in 1983, it provides information needed to understand both the theory and the practice of these methods and provides pseudocode for the problems. The algorithms covered are all based on Newton's method or "quasi-Newton" methods, and the heart of the book is the material on computational methods for multidimensional unconstrained optimization and nonlinear equation problems. The republication of this book by SIAM is driven by a continuing demand for specific and sound advice on how to solve real problems. The level of presentation is consistent throughout, with a good mix of examples and theory, making it a valuable text at both the graduate and undergraduate level. It has been praised as excellent for courses with approximately the same name as the book title and would also be useful as a supplemental text for a nonlinear programming or a numerical analysis course. Many exercises are provided to illustrate and develop the ideas in the text. A large appendix provides a mechanism for class projects and a reference for readers who want the details of the algorithms. Practitioners may use this book for self-study and reference. For complete understanding, readers should have a background in calculus and linear algebra. The book does contain background material in multivariable calculus and numerical linear algebra.

Author : Gabriele Ciaramella,Martin J. Gander
Publisher : SIAM
Page : 285 pages
File Size : 49,8 Mb
Release : 2022-02-08
Category : Mathematics
ISBN : 9781611976908

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Iterative Methods and Preconditioners for Systems of Linear Equations by Gabriele Ciaramella,Martin J. Gander Pdf

Iterative methods use successive approximations to obtain more accurate solutions. This book gives an introduction to iterative methods and preconditioning for solving discretized elliptic partial differential equations and optimal control problems governed by the Laplace equation, for which the use of matrix-free procedures is crucial. All methods are explained and analyzed starting from the historical ideas of the inventors, which are often quoted from their seminal works. Iterative Methods and Preconditioners for Systems of Linear Equations grew out of a set of lecture notes that were improved and enriched over time, resulting in a clear focus for the teaching methodology, which derives complete convergence estimates for all methods, illustrates and provides MATLAB codes for all methods, and studies and tests all preconditioners first as stationary iterative solvers. This textbook is appropriate for undergraduate and graduate students who want an overview or deeper understanding of iterative methods. Its focus on both analysis and numerical experiments allows the material to be taught with very little preparation, since all the arguments are self-contained, and makes it appropriate for self-study as well. It can be used in courses on iterative methods, Krylov methods and preconditioners, and numerical optimal control. Scientists and engineers interested in new topics and applications will also find the text useful.

Author : Samuel L. S. Jacoby,Janusz S. Kowalik,J. T. Pizzo
Publisher : Prentice Hall
Page : 294 pages
File Size : 41,8 Mb
Release : 1972
Category : Mathematics
ISBN : UOM:39015000510977

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Iterative Methods for Nonlinear Optimization Problems by Samuel L. S. Jacoby,Janusz S. Kowalik,J. T. Pizzo Pdf

Author : Charles L. Byrne
Publisher : A K Peters/CRC Press
Page : 408 pages
File Size : 53,5 Mb
Release : 2008
Category : Mathematics
ISBN : UOM:39076002783863

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Applied Iterative Methods by Charles L. Byrne Pdf

This book is a collection of essays on iterative algorithms and their uses. It focuses on the mathematics of medical image reconstruction, with emphasis on Fourier inversion. The book discusses the problems and algorithms in the context of operators on finite-dimensional Euclidean space.

Author : Amir Beck
Publisher : SIAM
Page : 476 pages
File Size : 50,7 Mb
Release : 2017-10-02
Category : Mathematics
ISBN : 9781611974980

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First-Order Methods in Optimization by Amir Beck Pdf

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 : Manfred Gilli,Dietmar Maringer,Enrico Schumann
Publisher : Academic Press
Page : 638 pages
File Size : 54,8 Mb
Release : 2019-08-30
Category : Electronic
ISBN : 9780128150658

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Numerical Methods and Optimization in Finance by Manfred Gilli,Dietmar Maringer,Enrico Schumann Pdf

Computationally-intensive tools play an increasingly important role in financial decisions. Many financial problems-ranging from asset allocation to risk management and from option pricing to model calibration-can be efficiently handled using modern computational techniques. Numerical Methods and Optimization in Finance presents such computational techniques, with an emphasis on simulation and optimization, particularly so-called heuristics. This book treats quantitative analysis as an essentially computational discipline in which applications are put into software form and tested empirically. This revised edition includes two new chapters, a self-contained tutorial on implementing and using heuristics, and an explanation of software used for testing portfolio-selection models. Postgraduate students, researchers in programs on quantitative and computational finance, and practitioners in banks and other financial companies can benefit from this second edition of Numerical Methods and Optimization in Finance. Introduces numerical methods to readers with economics backgrounds Emphasizes core simulation and optimization problems Includes MATLAB and R code for all applications, with sample code in the text and freely available for download

Author : Sergiy Butenko,Panos M. Pardalos
Publisher : CRC Press
Page : 408 pages
File Size : 47,5 Mb
Release : 2014-03-11
Category : Business & Economics
ISBN : 9781466577787

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Numerical Methods and Optimization by Sergiy Butenko,Panos M. Pardalos Pdf

For students in industrial and systems engineering (ISE) and operations research (OR) to understand optimization at an advanced level, they must first grasp the analysis of algorithms, computational complexity, and other concepts and modern developments in numerical methods. Satisfying this prerequisite, Numerical Methods and Optimization: An Intro

Author : Charles L. Byrne
Publisher : CRC Press
Page : 302 pages
File Size : 44,7 Mb
Release : 2014-02-12
Category : Business & Economics
ISBN : 9781482222333

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Iterative Optimization in Inverse Problems by Charles L. Byrne Pdf

Iterative Optimization in Inverse Problems brings together a number of important iterative algorithms for medical imaging, optimization, and statistical estimation. It incorporates recent work that has not appeared in other books and draws on the author’s considerable research in the field, including his recently developed class of SUMMA algorithms. Related to sequential unconstrained minimization methods, the SUMMA class includes a wide range of iterative algorithms well known to researchers in various areas, such as statistics and image processing. Organizing the topics from general to more specific, the book first gives an overview of sequential optimization, the subclasses of auxiliary-function methods, and the SUMMA algorithms. The next three chapters present particular examples in more detail, including barrier- and penalty-function methods, proximal minimization, and forward-backward splitting. The author also focuses on fixed-point algorithms for operators on Euclidean space and then extends the discussion to include distance measures other than the usual Euclidean distance. In the final chapters, specific problems illustrate the use of iterative methods previously discussed. Most chapters contain exercises that introduce new ideas and make the book suitable for self-study. Unifying a variety of seemingly disparate algorithms, the book shows how to derive new properties of algorithms by comparing known properties of other algorithms. This unifying approach also helps researchers—from statisticians working on parameter estimation to image scientists processing scanning data to mathematicians involved in theoretical and applied optimization—discover useful related algorithms in areas outside of their expertise.