Iterative Methods for Optimization


Author: C. T. Kelley
Publisher: SIAM
ISBN: 9781611970920
Category: Iterative methods (Mathematics)
Page: 180
View: 3570

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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.

Computational Methods for Inverse Problems


Author: Curtis R. Vogel
Publisher: SIAM
ISBN: 0898715504
Category: Mathematics
Page: 183
View: 4528

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Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.

Optimization Software Guide


Author: Jorge J. More,Stephen J. Wright
Publisher: SIAM
ISBN: 0898713226
Category: Mathematics
Page: 154
View: 7154

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Mathematics of Computing -- Numerical Analysis.

Solving Nonlinear Equations with Newton's Method


Author: C. T. Kelley
Publisher: SIAM
ISBN: 9780898718898
Category: Iterative methods (Mathematics)
Page: 104
View: 1788

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This book on Newton's method is a user-oriented guide to algorithms and implementation. In just over 100 pages, it shows, via algorithms in pseudocode, in MATLAB, and with several examples, how one can choose an appropriate Newton-type method for a given problem, diagnose problems, and write an efficient solver or apply one written by others. It contains trouble-shooting guides to the major algorithms, their most common failure modes, and the likely causes of failure. It also includes many worked-out examples (available on the SIAM website) in pseudocode and a collection of MATLAB codes, allowing readers to experiment with the algorithms easily and implement them in other languages.

Numerical Methods for Unconstrained Optimization and Nonlinear Equations


Author: J. E. Dennis, Jr.,Robert B. Schnabel
Publisher: SIAM
ISBN: 9781611971200
Category: Equations
Page: 378
View: 6873

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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.

Computational Methods for Option Pricing


Author: Yves Achdou,Olivier Pironneau
Publisher: SIAM
ISBN: 0898715733
Category: Technology & Engineering
Page: 297
View: 5868

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This book allows you to understand fully the modern tools of numerical analysis in finance.

A Panorama of Mathematics: Pure and Applied


Author: Carlos M. da Fonseca,Dinh Van Huynh,Steve Kirkland,Vu Kim Tuan
Publisher: American Mathematical Soc.
ISBN: 1470416689
Category: Mathematics
Page: 279
View: 3665

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This volume contains the proceedings of the Conference on Mathematics and its Applications-2014, held from November 14-17, 2014, at Kuwait University, Safat, Kuwait. Papers contained in this volume cover various topics in pure and applied mathematics ranging from an introductory study of quotients and homomorphisms of C-systems, also known as contextual pre-categories, to the most important consequences of the so-called Fokas method. Also covered are multidisciplinary topics such as new structural and spectral matricial results, acousto-electromagnetic tomography method, a recent hybrid imaging technique, some numerical aspects of sonic-boom minimization, PDE eigenvalue problems, von Neumann entropy in graph theory, the relative entropy method for hyperbolic systems, conductances on grids, inverse problems in magnetohydrodynamics, location and size estimation of small rigid bodies using elastic far-fields, and the space-time fractional Schrödinger equation, just to cite a few. Papers contained in this volume cover various topics in pure and applied mathematics ranging from an introductory study of quotients and homomorphisms of C-systems, also known as contextual pre-categories, to the most important consequences of the so-called Fokas method. Also covered are multidisciplinary topics such as new structural and spectral matricial results, acousto-electromagnetic tomography method, a recent hybrid imaging technique, some numerical aspects of sonic-boom minimization, PDE eigenvalue problems, von Neumann entropy in graph theory, the relative entropy method for hyperbolic systems, conductances on grids, inverse problems in magnetohydrodynamics, location and size estimation of small rigid bodies using elastic far-fields, and the space-time fractional Schrödinger equation, just to cite a few. - See more at: http://s350148651-preview.tizrapublisher.com/conm-658/#sthash.74nRhV3y.dpufThis volume contains the proceedings of the Conference on Mathematics and its Applications–2014, held from November 14–17, 2014, at Kuwait University, Safat, Kuwait. - See more at: http://s350148651-preview.tizrapublisher.com/conm-658/#sthash.74nRhV3y.dpuf

Numerical Continuation Methods

An Introduction
Author: Eugene L. Allgower,Kurt Georg
Publisher: Springer Science & Business Media
ISBN: 3642612571
Category: Mathematics
Page: 388
View: 7215

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Over the past fifteen years two new techniques have yielded extremely important contributions toward the numerical solution of nonlinear systems of equations. This book provides an introduction to and an up-to-date survey of numerical continuation methods (tracing of implicitly defined curves) of both predictor-corrector and piecewise-linear types. It presents and analyzes implementations aimed at applications to the computation of zero points, fixed points, nonlinear eigenvalue problems, bifurcation and turning points, and economic equilibria. Many algorithms are presented in a pseudo code format. An appendix supplies five sample FORTRAN programs with numerical examples, which readers can adapt to fit their purposes, and a description of the program package SCOUT for analyzing nonlinear problems via piecewise-linear methods. An extensive up-to-date bibliography spanning 46 pages is included. The material in this book has been presented to students of mathematics, engineering and sciences with great success, and will also serve as a valuable tool for researchers in the field.

Computational Optimization of Systems Governed by Partial Differential Equations


Author: Alfio Borzi,Volker Schulz
Publisher: SIAM
ISBN: 9781611972054
Category: Differential equations, Partial
Page: 282
View: 8775

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This book fills a gap between theory-oriented investigations in PDE-constrained optimization and the practical demands made by numerical solutions of PDE optimization problems. The authors discuss computational techniques representing recent developments that result from a combination of modern techniques for the numerical solution of PDEs and for sophisticated optimization schemes. The book offers readers a combined treatment of PDE-constrained optimization and uncertainties and an extensive discussion of multigrid optimization. It provides a bridge between continuous optimization and PDE modeling and focuses on the numerical solution of the corresponding problems.

Identification of Continuous-time Models from Sampled Data


Author: Hugues Garnier,Liuping Wang
Publisher: Springer Science & Business Media
ISBN: 9781848001619
Category: Technology & Engineering
Page: 413
View: 2807

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This is the first book dedicated to direct continuous-time model identification for 15 years. It cuts down on time spent hunting through journals by providing an overview of much recent research in an increasingly busy field. The CONTSID toolbox discussed in the final chapter gives an overview of developments and practical examples in which MATLAB® can be used for direct time-domain identification of continuous-time systems. This is a valuable reference for a broad audience.

Evaluating Derivatives

Principles and Techniques of Algorithmic Differentiation, Second Edition
Author: Andreas Griewank,Andrea Walther
Publisher: SIAM
ISBN: 0898716594
Category: Mathematics
Page: 438
View: 2008

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This title is a comprehensive treatment of algorithmic, or automatic, differentiation. The second edition covers recent developments in applications and theory, including an elegant NP completeness argument and an introduction to scarcity.

Multilevel Adaptive Methods for Partial Differential Equations


Author: Stephen F. McCormick
Publisher: SIAM
ISBN: 0898712475
Category: Mathematics
Page: 162
View: 7054

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A practical handbook for understanding and using fast adaptive composite grid (FAC) methods for discretization and solution of partial differential equations (PDEs). Contains fundamental concepts. These so-called FAC are characterized by their use of a composite grid, which is nominally the union of various uniform grids. FAC is capable of producing a composite grid with tailored resolution, and a corresponding solution with commensurate accuracy, at a cost proportional to the number of composite grid points. Moreover, special asynchronous versions of the fast adaptive composite grid methods (AFAC) studied here have seemingly optimal complexity in a parallel computing environment. Most of the methods treated in this book were discovered only within the last decade, and in many cases their development is still in its infancy. While this is not meant to be comprehensive, it does provide a theoretical and practical guide to multilevel adaptive methods and relevant discretization techniques.

Some Topics in Industrial and Applied Mathematics


Author: Rolf Jeltsch,I. H. Sloan
Publisher: World Scientific
ISBN: 9812709347
Category: Mathematics
Page: 218
View: 9414

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The Shanghai Forum on Industrial and Applied Mathematics was organized in May 2006 on the occasion that many famous industrial and applied mathematicians gathered in Shanghai from different countries to participate in the Officers' Meeting and the Board Meeting of the ICIAM (International Council for Industrial and Applied Mathematics). This volume collects the material covered by the majority of the lectures of which reflects panoramically recent results and trends in industrial and applied mathematics. This book will be very useful for graduate students and researchers in industrial and applied mathematics.

Handbook for Matrix Computations


Author: Thomas F. Coleman,Charles Van Loan
Publisher: SIAM
ISBN: 9781611971040
Category: Matrices
Page: 264
View: 4197

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Provides the user with a step-by-step introduction to Fortran 77, BLAS, LINPACK, and MATLAB. It is a reference that spans several levels of practical matrix computations with a strong emphasis on examples and "hands on" experience.

The Mathematics of Reservoir Simulation


Author: Richard E. Ewing
Publisher: SIAM
ISBN: 0898716624
Category: Science
Page: 186
View: 942

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This book describes the state of the art of the mathematical theory and numerical analysis of imaging. Some of the applications covered in the book include computerized tomography, magnetic resonance imaging, emission tomography, electron microscopy, ultrasound transmission tomography, industrial tomography, seismic tomography, impedance tomography, and NIR imaging.

Numerical Methods of Mathematical Optimization

With ALGOL and FORTRAN Programs
Author: Hans P. Künzi,H. G. Tzschach,C. A. Zehnder
Publisher: Academic Press
ISBN: 1483264718
Category: Mathematics
Page: 222
View: 8127

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Numerical Methods of Mathematical Optimization: With ALGOL and FORTRAN Programs reviews the theory and the practical application of the numerical methods of mathematical optimization. An ALGOL and a FORTRAN program was developed for each one of the algorithms described in the theoretical section. This should result in easy access to the application of the different optimization methods. Comprised of four chapters, this volume begins with a discussion on the theory of linear and nonlinear optimization, with the main stress on an easily understood, mathematically precise presentation. In addition to the theoretical considerations, several algorithms of importance to the numerical application of optimization theory are described. The next chapter explains the computer programs used in actual optimization, which have the form of procedures or subroutines. The book concludes with an analysis of ALGOL and FORTRAN, paying particular attention to their use in global optimization procedures as well as for the simplex and duoplex methods and the decomposition, Gomory, Beale, and Wolfe algorithms. This monograph will be helpful to students and practitioners of computer science and applied mathematics.

A Mathematical View of Interior-point Methods in Convex Optimization


Author: James Renegar
Publisher: SIAM
ISBN: 9780898718812
Category: Convex programming
Page: 117
View: 6232

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Here is a book devoted to well-structured and thus efficiently solvable convex optimization problems, with emphasis on conic quadratic and semidefinite programming. The authors present the basic theory underlying these problems as well as their numerous applications in engineering, including synthesis of filters, Lyapunov stability analysis, and structural design. The authors also discuss the complexity issues and provide an overview of the basic theory of state-of-the-art polynomial time interior point methods for linear, conic quadratic, and semidefinite programming. The book's focus on well-structured convex problems in conic form allows for unified theoretical and algorithmical treatment of a wide spectrum of important optimization problems arising in applications.