Introduction to Optimization

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Author: Pablo Pedregal

Publisher: Springer Science & Business Media

ISBN: 0387216804

Category: Mathematics

Page: 246

View: 4244

This undergraduate textbook introduces students of science and engineering to the fascinating field of optimization. It is a unique book that brings together the subfields of mathematical programming, variational calculus, and optimal control, thus giving students an overall view of all aspects of optimization in a single reference. As a primer on optimization, its main goal is to provide a succinct and accessible introduction to linear programming, nonlinear programming, numerical optimization algorithms, variational problems, dynamic programming, and optimal control. Prerequisites have been kept to a minimum, although a basic knowledge of calculus, linear algebra, and differential equations is assumed.

Introduction to Numerical Linear Algebra and Optimisation

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Author: Philippe G. Ciarlet,Bernadette Miara,Jean-Marie Thomas

Publisher: Cambridge University Press

ISBN: 9780521339841

Category: Computers

Page: 436

View: 6092

Based on courses taught to advanced undergraduate students, this book offers a broad introduction to the methods of numerical linear algebra and optimization. The prerequisites are familiarity with the basic properties of matrices, finite-dimensional vector spaces and advanced calculus, and some exposure to fundamental notions from functional analysis. The book is divided into two parts. The first part deals with numerical linear algebra (numerical analysis of matrices, direct and indirect methods for solving linear systems, calculation of eigenvalues and eigenvectors) and the second, optimizations (general algorithms, linear and nonlinear programming). Summaries of basic mathematics are provided, proof of theorems are complete yet kept as simple as possible, applications from physics and mechanics are discussed, a great many exercises are included, and there is a useful guide to further reading.

Numerical Analysis and Optimization

An Introduction to Mathematical Modelling and Numerical Simulation

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Author: Grégoire Allaire

Publisher: Oxford University Press

ISBN: 0199205213

Category: Mathematics

Page: 455

View: 8312

This work familiarises students with mathematical models (PDEs) and methods of numerical solution and optimisation. Including numerous exercises and examples, this is an ideal text for advanced students in Applied Mathematics, Engineering, Physical Science and Computer Science.

Introduction to Uncertainty Quantification

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Author: T.J. Sullivan

Publisher: Springer

ISBN: 3319233955

Category: Mathematics

Page: 342

View: 6881

This text provides a framework in which the main objectives of the field of uncertainty quantification (UQ) are defined and an overview of the range of mathematical methods by which they can be achieved. Complete with exercises throughout, the book will equip readers with both theoretical understanding and practical experience of the key mathematical and algorithmic tools underlying the treatment of uncertainty in modern applied mathematics. Students and readers alike are encouraged to apply the mathematical methods discussed in this book to their own favorite problems to understand their strengths and weaknesses, also making the text suitable for a self-study. Uncertainty quantification is a topic of increasing practical importance at the intersection of applied mathematics, statistics, computation and numerous application areas in science and engineering. This text is designed as an introduction to UQ for senior undergraduate and graduate students with a mathematical or statistical background and also for researchers from the mathematical sciences or from applications areas who are interested in the field. T. J. Sullivan was Warwick Zeeman Lecturer at the Mathematics Institute of the University of Warwick, United Kingdom, from 2012 to 2015. Since 2015, he is Junior Professor of Applied Mathematics at the Free University of Berlin, Germany, with specialism in Uncertainty and Risk Quantification.

Optimization

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Author: Kenneth Lange

Publisher: Springer Science & Business Media

ISBN: 1461458382

Category: Mathematics

Page: 529

View: 6069

Finite-dimensional optimization problems occur throughout the mathematical sciences. The majority of these problems cannot be solved analytically. This introduction to optimization attempts to strike a balance between presentation of mathematical theory and development of numerical algorithms. Building on students’ skills in calculus and linear algebra, the text provides a rigorous exposition without undue abstraction. Its stress on statistical applications will be especially appealing to graduate students of statistics and biostatistics. The intended audience also includes students in applied mathematics, computational biology, computer science, economics, and physics who want to see rigorous mathematics combined with real applications. In this second edition the emphasis remains on finite-dimensional optimization. New material has been added on the MM algorithm, block descent and ascent, and the calculus of variations. Convex calculus is now treated in much greater depth. Advanced topics such as the Fenchel conjugate, subdifferentials, duality, feasibility, alternating projections, projected gradient methods, exact penalty methods, and Bregman iteration will equip students with the essentials for understanding modern data mining techniques in high dimensions.

Introduction to Scientific Computing and Data Analysis

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Author: Mark H. Holmes

Publisher: Springer

ISBN: 3319302566

Category: Computers

Page: 497

View: 9709

This textbook provides and introduction to numerical computing and its applications in science and engineering. The topics covered include those usually found in an introductory course, as well as those that arise in data analysis. This includes optimization and regression based methods using a singular value decomposition. The emphasis is on problem solving, and there are numerous exercises throughout the text concerning applications in engineering and science. The essential role of the mathematical theory underlying the methods is also considered, both for understanding how the method works, as well as how the error in the computation depends on the method being used. The MATLAB codes used to produce most of the figures and data tables in the text are available on the author’s website and SpringerLink.

Introduction to Dynamic Programming

International Series in Modern Applied Mathematics and Computer Science

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Author: Leon Cooper,Mary W. Cooper

Publisher: Elsevier

ISBN: 1483136620

Category: Mathematics

Page: 300

View: 2233

Introduction to Dynamic Programming introduces the reader to dynamic programming and presents the underlying mathematical ideas and results, as well as the application of these ideas to various problem areas. A large number of solved practical problems and computational examples are included to clarify the way dynamic programming is used to solve problems. A consistent notation is applied throughout the text for the expression of quantities such as state variables and decision variables. This monograph consists of 10 chapters and opens with an overview of dynamic programming as a particular approach to optimization, along with the basic components of any mathematical optimization model. The following chapters discuss the application of dynamic programming to variational problems; functional equations and the principle of optimality; reduction of state dimensionality and approximations; and stochastic processes and the calculus of variations. The final chapter looks at several actual applications of dynamic programming to practical problems, such as animal feedlot optimization and optimal scheduling of excess cash investment. This book should be suitable for self-study or for use as a text in a one-semester course on dynamic programming at the senior or first-year, graduate level for students of mathematics, statistics, operations research, economics, business, industrial engineering, or other engineering fields.

An Introduction to Scientific Computing

Twelve Computational Projects Solved with MATLAB

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Author: Ionut Danaila,Pascal Joly,Sidi Mahmoud Kaber,Marie Postel

Publisher: Springer Science & Business Media

ISBN: 038730889X

Category: Mathematics

Page: 294

View: 8453

This book demonstrates scientific computing by presenting twelve computational projects in several disciplines including Fluid Mechanics, Thermal Science, Computer Aided Design, Signal Processing and more. Each follows typical steps of scientific computing, from physical and mathematical description, to numerical formulation and programming and critical discussion of results. The text teaches practical methods not usually available in basic textbooks: numerical checking of accuracy, choice of boundary conditions, effective solving of linear systems, comparison to exact solutions and more. The final section of each project contains the solutions to proposed exercises and guides the reader in using the MATLAB scripts available online.

Introduction to Nonlinear Optimization

Theory, Algorithms, and Applications with MATLAB

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Author: Amir Beck

Publisher: SIAM

ISBN: 1611973651

Category: Mathematics

Page: 282

View: 3467

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.

Newsletter

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Author: New Zealand Mathematical Society

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 5282

Optimization Techniques

An Introduction

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Author: L. R. Foulds

Publisher: Springer Science & Business Media

ISBN: 1461394589

Category: Science

Page: 502

View: 5116

Optimization is the process by which the optimal solution to a problem, or optimum, is produced. The word optimum has come from the Latin word optimus, meaning best. And since the beginning of his existence Man has strived for that which is best. There has been a host of contributions, from Archimedes to the present day, scattered across many disciplines. Many of the earlier ideas, although interesting from a theoretical point of view, were originally of little practical use, as they involved a daunting amount of com putational effort. Now modern computers perform calculations, whose time was once estimated in man-years, in the figurative blink of an eye. Thus it has been worthwhile to resurrect many of these earlier methods. The advent of the computer has helped bring about the unification of optimization theory into a rapidly growing branch of applied mathematics. The major objective of this book is to provide an introduction to the main optimization tech niques which are at present in use. It has been written for final year undergrad uates or first year graduates studying mathematics, engineering, business, or the physical or social sciences. The book does not assume much mathemati cal knowledge. It has an appendix containing the necessary linear algebra and basic calculus, making it virtually self-contained. This text evolved out of the experience of teaching the material to finishing undergraduates and beginning graduates.

Optimization and Approximation

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Author: Pablo Pedregal

Publisher: Springer

ISBN: 3319648438

Category: Mathematics

Page: 254

View: 4374

This book provides a basic, initial resource, introducing science and engineering students to the field of optimization. It covers three main areas: mathematical programming, calculus of variations and optimal control, highlighting the ideas and concepts and offering insights into the importance of optimality conditions in each area. It also systematically presents affordable approximation methods. Exercises at various levels have been included to support the learning process.

An Introduction to Unconstrained Optimisation

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Author: J McKeown,D Meegan,D Sprevak

Publisher: CRC Press

ISBN: 9780750300254

Category: Mathematics

Page: 160

View: 5775

Integrating computer graphics and computer-based exercises with the text, An Introduction to Unconstrained Optimisation illustrates key methods with many examples and exercises using the computer. The book takes an elementary approach to this advanced topic, allowing readers to concentrate on learning and understanding the concepts of numerical optimization without unnecessary involvement in the intricacies of the subject. In addition, the modular approach of the software provides the opportunity to explore the algorithms used and to develop them further or try alternative approaches. Most of the algorithms are based upon a "hill-climbing" concept which, in two dimensions, is illustrated dynamically on the computer screen in the form of contour plots and search directions. The text is not specific to any particular microcomputer. Software is available for the BBC series of machines (40/80 track disc formats) and PC-compatible machines. The software is not available from your local bookstore, but is easily obtainable using the order form in the book. Keeping proofs and lists of methods to a minimum, the book is at a level suitable for a first course in numerical analysis, with a basic knowledge of calculus and vector algebra assumed. This book/software package will be of interest to professionals, teachers, and undergraduate students in mathematics, operational research, science, and engineering as well as economics and management courses that deal with quantitative methods.

A Gentle Introduction to Optimization

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Author: B. Guenin,J. Könemann,L. Tunçel

Publisher: Cambridge University Press

ISBN: 1107053447

Category: Business & Economics

Page: 282

View: 410

Assuming only basic linear algebra, this textbook is the perfect starting point for undergraduate students from across the mathematical sciences.

Introduction to Global Optimization Exploiting Space-Filling Curves

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Author: Yaroslav D. Sergeyev,Roman G. Strongin,Daniela Lera

Publisher: Springer Science & Business Media

ISBN: 1461480426

Category: Mathematics

Page: 125

View: 4369

Introduction to Global Optimization Exploiting Space-Filling Curves provides an overview of classical and new results pertaining to the usage of space-filling curves in global optimization. The authors look at a family of derivative-free numerical algorithms applying space-filling curves to reduce the dimensionality of the global optimization problem; along with a number of unconventional ideas, such as adaptive strategies for estimating Lipschitz constant, balancing global and local information to accelerate the search. Convergence conditions of the described algorithms are studied in depth and theoretical considerations are illustrated through numerical examples. This work also contains a code for implementing space-filling curves that can be used for constructing new global optimization algorithms. Basic ideas from this text can be applied to a number of problems including problems with multiextremal and partially defined constraints and non-redundant parallel computations can be organized. Professors, students, researchers, engineers, and other professionals in the fields of pure mathematics, nonlinear sciences studying fractals, operations research, management science, industrial and applied mathematics, computer science, engineering, economics, and the environmental sciences will find this title useful . ​

An Introduction to Mathematical Modeling

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Author: Edward A. Bender

Publisher: Courier Corporation

ISBN: 9780486411804

Category: Mathematics

Page: 256

View: 5507

Accessible text features over 100 reality-based examples pulled from the science, engineering and operations research fields. Prerequisites: ordinary differential equations, continuous probability. Numerous references. Includes 27 black-and-white figures. 1978 edition.

From Vector Spaces to Function Spaces

Introduction to Functional Analysis with Applications

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Author: Yutaka Yamamoto

Publisher: SIAM

ISBN: 1611972302

Category: Mathematics

Page: 260

View: 8025

A guide to analytic methods in applied mathematics from the perspective of functional analysis, suitable for scientists, engineers and students.