Introduction to Optimization

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Author: Pablo Pedregal

Publisher: Springer Science & Business Media

ISBN: 0387216804

Category: Mathematics

Page: 246

View: 6141

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: 8192

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.

Introduction to Uncertainty Quantification

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Author: T.J. Sullivan

Publisher: Springer

ISBN: 3319233955

Category: Mathematics

Page: 342

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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 and Approximation

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Author: Pablo Pedregal

Publisher: Springer

ISBN: 3319648438

Category: Mathematics

Page: 254

View: 5913

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.

Newsletter

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Author: New Zealand Mathematical Society

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 5266

Optimization Techniques

An Introduction

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Author: L. R. Foulds

Publisher: Springer Science & Business Media

ISBN: 1461394589

Category: Science

Page: 502

View: 4637

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

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Author: Kenneth Lange

Publisher: Springer Science & Business Media

ISBN: 1475741820

Category: Mathematics

Page: 255

View: 4733

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.

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: 6713

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.

Functional Analysis and Applied Optimization in Banach Spaces

Applications to Non-Convex Variational Models

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Author: Fabio Botelho

Publisher: Springer

ISBN: 3319060740

Category: Mathematics

Page: 560

View: 9388

​This book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physics and engineering problems. The book includes introductory and advanced concepts in measure and integration, as well as an introduction to Sobolev spaces. The problems presented are nonlinear, with non-convex variational formulation. Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to an appropriate weak cluster point of minimizing sequences for the primal one. Indeed, the dual approach more readily facilitates numerical computations for some of the selected models. While intended primarily for applied mathematicians, the text will also be of interest to engineers, physicists, and other researchers in related fields.

Introduction to Scientific Computing and Data Analysis

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Author: Mark H. Holmes

Publisher: Springer

ISBN: 3319302566

Category: Computers

Page: 497

View: 2007

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: 9010

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.

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: 7223

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

Introduction to Computational Social Science

Principles and Applications

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Author: Claudio Cioffi-Revilla

Publisher: Springer Science & Business Media

ISBN: 1447156617

Category: Computers

Page: 320

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This reader-friendly textbook is the first work of its kind to provide a unified Introduction to Computational Social Science (CSS). Four distinct methodological approaches are examined in detail, namely automated social information extraction, social network analysis, social complexity theory and social simulation modeling. The coverage of these approaches is supported by a discussion of the historical context, as well as by a list of texts for further reading. Features: highlights the main theories of the CSS paradigm as causal explanatory frameworks that shed new light on the nature of human and social dynamics; explains how to distinguish and analyze the different levels of analysis of social complexity using computational approaches; discusses a number of methodological tools; presents the main classes of entities, objects and relations common to the computational analysis of social complexity; examines the interdisciplinary integration of knowledge in the context of social phenomena.

Taschenbuch der Mathematik

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Author: Eberhard Zeidler,Wolfgang Hackbusch

Publisher: Springer-Verlag

ISBN: 3835101234

Category: Mathematics

Page: 1310

View: 8488

Das Vieweg+Teubner Taschenbuch der Mathematik erfüllt aktuell, umfassend und kompakt alle Erwartungen, die an ein mathematisches Nachschlagewerk gestellt werden. Es vermittelt ein lebendiges und modernes Bild der heutigen Mathematik. Als Taschenbuch begleitet es die Bachelor-Studierenden vom ersten Semester bis zur letzten Prüfung und der Praktiker nutzt es als ständiges und unentbehrliches Nachschlagewerk in seinem Berufsalltag. Das Taschenbuch bietet alles, was in Bachelor-Studiengängen im Haupt- und Nebenfach Mathematik benötigt wird. Der Text für diese Ausgabe wurde stark überarbeitet. Zu spezielle Inhalte wurden herausgenommen und dafür Themen der Wirtschaftsmathematik und Algorithmik hinzugenommen. Das Vieweg+Teubner Handbuch der Mathematik (eAusgabe) enthält darüberhinaus ergänzendes und weiterführendes Material für das Masterstudium.

Springer-Handbuch der Mathematik III

Begründet von I.N. Bronstein und K.A. Semendjaew Weitergeführt von G. Grosche, V. Ziegler und D. Ziegler Herausgegeben von E. Zeidler

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Author: Eberhard Zeidler

Publisher: Springer-Verlag

ISBN: 3658002751

Category: Mathematics

Page: 529

View: 7291

Als mehrbändiges Nachschlagewerk ist das Springer-Handbuch der Mathematik in erster Linie für wissenschaftliche Bibliotheken, akademische Institutionen und Firmen sowie interessierte Individualkunden in Forschung und Lehre gedacht. Es ergänzt das einbändige themenumfassende Springer-Taschenbuch der Mathematik (ehemaliger Titel Teubner-Taschenbuch der Mathematik), das sich in seiner begrenzten Stoffauswahl besonders an Studierende richtet. Teil III des Springer-Handbuchs enthält neben den Kapiteln 5-9 des Springer-Taschenbuchs zusätzliches Material zu stochastischen Prozessen.​

Power Generation, Operation, and Control

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Author: Allen J. Wood,Bruce F. Wollenberg,Gerald B. Sheblé

Publisher: John Wiley & Sons

ISBN: 1118733916

Category: Technology & Engineering

Page: 656

View: 3021

A thoroughly revised new edition of the definitive work on power systems best practices In this eagerly awaited new edition, Power Generation, Operation, and Control continues to provide engineers and academics with a complete picture of the techniques used in modern power system operation. Long recognized as the standard reference in the field, the book has been thoroughly updated to reflect the enormous changes that have taken place in the electric power industry since the Second Edition was published seventeen years ago. With an emphasis on both the engineering and economic aspects of energy management, the Third Edition introduces central "terminal" characteristics for thermal and hydroelectric power generation systems, along with new optimization techniques for tackling real-world operating problems. Readers will find a range of algorithms and methods for performing integrated economic, network, and generating system analysis, as well as modern methods for power system analysis, operation, and control. Special features include: State-of-the-art topics such as market simulation, multiple market analysis, contract and market bidding, and other business topics Chapters on generation with limited energy supply, power flow control, power system security, and more An introduction to regulatory issues, renewable energy, and other evolving topics New worked examples and end-of-chapter problems A companion website with additional materials, including MATLAB programs and power system sample data sets