Variational Methods in Optimization

Highly readable text elucidates applications of the chain rule of differentiation, integration by parts, parametric curves, line integrals, double integrals, and elementary differential equations. 1974 edition.

Author: Donald R. Smith

Publisher: Courier Corporation

ISBN: 0486404552

Category: Mathematics

Page: 378

View: 982

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Highly readable text elucidates applications of the chain rule of differentiation, integration by parts, parametric curves, line integrals, double integrals, and elementary differential equations. 1974 edition.
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Variational Methods for Structural Optimization

This book bridges a gap between a rigorous mathematical approach to variational problems and the practical use of algorithms of structural optimization in engineering applications.

Author: Andrej Cherkaev

Publisher: Springer Science & Business Media

ISBN: 9781461211884

Category: Science

Page: 548

View: 483

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This book bridges a gap between a rigorous mathematical approach to variational problems and the practical use of algorithms of structural optimization in engineering applications. The foundations of structural optimization are presented in sufficiently simple form as to make them available for practical use.
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Variational Methods in Nonlinear Analysis

This well-thought-out book covers the fundamentals of nonlinear analysis, with a particular focus on variational methods and their applications.

Author: Dimitrios C. Kravvaritis

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 9783110647457

Category: Mathematics

Page: 499

View: 213

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This well-thought-out book covers the fundamentals of nonlinear analysis, with a particular focus on variational methods and their applications. Starting from preliminaries in functional analysis, it expands in several directions such as Banach spaces, fixed point theory, nonsmooth analysis, minimax theory, variational calculus and inequalities, critical point theory, monotone, maximal monotone and pseudomonotone operators, and evolution problems.
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Variational Methods in Shape Optimization Problems

In this work these problems are treated from both the classical and modern perspectives and target a broad audience of graduate students in pure and applied mathematics, as well as engineers requiring a solid mathematical basis for the ...

Author: Dorin Bucur

Publisher: Springer Science & Business Media

ISBN: 9780817644031

Category: Mathematics

Page: 216

View: 452

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Shape optimization problems are treated from the classical and modern perspectives Targets a broad audience of graduate students in pure and applied mathematics, as well as engineers requiring a solid mathematical basis for the solution of practical problems Requires only a standard knowledge in the calculus of variations, differential equations, and functional analysis Driven by several good examples and illustrations Poses some open questions.
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Optimization by Variational Methods

7 The Linear Regulator Problem BIBLIOGRAPHICAL NOTES PROBLEMS 394
398 400 402 405 407 407 Name Index 411 Subject Index 415 Vari optimization
by Optimization by Variational Methods OPTIMIZATION AND ENGINEERING Xvi
 ...

Author: Morton M. Denn

Publisher:

ISBN: UOM:39015013050920

Category: Calculus of variations

Page: 419

View: 102

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Nonlinear Functional Analysis and its Applications

The present English edition was translated from a completely rewritten manuscript which is significantly longer than the original version in the Teubner-Texte series.

Author: E. Zeidler

Publisher: Springer Science & Business Media

ISBN: 9781461250203

Category: Science

Page: 662

View: 893

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As long as a branch of knowledge offers an abundance of problems, it is full of vitality. David Hilbert Over the last 15 years I have given lectures on a variety of problems in nonlinear functional analysis and its applications. In doing this, I have recommended to my students a number of excellent monographs devoted to specialized topics, but there was no complete survey-type exposition of nonlinear functional analysis making available a quick survey to the wide range of readers including mathematicians, natural scientists, and engineers who have only an elementary knowledge of linear functional analysis. I have tried to close this gap with my five-part lecture notes, the first three parts of which have been published in the Teubner-Texte series by Teubner-Verlag, Leipzig, 1976, 1977, and 1978. The present English edition was translated from a completely rewritten manuscript which is significantly longer than the original version in the Teubner-Texte series. The material is organized in the following way: Part I: Fixed Point Theorems. Part II: Monotone Operators. Part III: Variational Methods and Optimization. Parts IV jV: Applications to Mathematical Physics. The exposition is guided by the following considerations: (a) What are the supporting basic ideas and what intrinsic interrelations exist between them? (/3) In what relation do the basic ideas stand to the known propositions of classical analysis and linear functional analysis? ( y) What typical applications are there? Vll Preface viii Special emphasis is placed on motivation.
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Variational Methods with Applications in Science and Engineering

This book reflects the strong connection between calculus of variations and the applications for which variational methods form the foundation.

Author: Kevin W. Cassel

Publisher: Cambridge University Press

ISBN: 9781107022584

Category: Mathematics

Page: 432

View: 396

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This book reflects the strong connection between calculus of variations and the applications for which variational methods form the foundation.
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Applied Functional Analysis and Variational Methods in Engineering

Reddy , J . N . : “ Energy and Variational Methods in Applied Mechanics ( with an
introduction to the finite element ... OPTIMIZATION ( Lagrange Multiplier and
Penalty Function Methods ) Bertsekas , D . P . : “ Constrained Optimization and ...

Author: Junuthula Narasimha Reddy

Publisher:

ISBN: STANFORD:36105023485589

Category: Technology & Engineering

Page: 546

View: 887

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Relaxation in Optimization Theory and Variational Calculus

Introduces applied mathematicians and graduate students to an original relaxation method based on a continuous extension of various optimization problems relating to convex compactification; it can be applied to problems in optimal control ...

Author: Tomáš Roubiček

Publisher: Walter de Gruyter

ISBN: 3110145421

Category: Mathematics

Page: 474

View: 559

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Introduces applied mathematicians and graduate students to an original relaxation method based on a continuous extension of various optimization problems relating to convex compactification; it can be applied to problems in optimal control theory, the calculus of variations, and non-cooperative game theory. Reviews the background and summarizes the general theory of convex compactifications, then uses it to obtain convex, locally compact envelopes of the Lebesague and Sobolev spaces involved in concrete problems. The nontrivial envelopes cover the classical Young measures as well as various generalizations of them, which can record the limit behavior of fast oscillation and concentration effects. Annotation copyrighted by Book News, Inc., Portland, OR
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Variational Methods in Partially Ordered Spaces

This book discusses basic tools of partially ordered spaces and applies them to variational methods in Nonlinear Analysis and for optimizing problems. This book is aimed at graduate students and research mathematicians.

Author: Alfred Göpfert

Publisher: Springer Science & Business Media

ISBN: 9780387217437

Category: Business & Economics

Page: 350

View: 428

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This book discusses basic tools of partially ordered spaces and applies them to variational methods in Nonlinear Analysis and for optimizing problems. This book is aimed at graduate students and research mathematicians.
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Variational Methods in Mathematics Science and Engineering

Hilbert space; Variational methods; Application of variational methods to the solution of boundary value problems in ordinary and partial differential equations; Theory of boundary value problems in differential equations based on the ...

Author: K. Rektorys

Publisher: Springer Science & Business Media

ISBN: 9027710600

Category: Mathematics

Page: 551

View: 729

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Hilbert space; Variational methods; Application of variational methods to the solution of boundary value problems in ordinary and partial differential equations; Theory of boundary value problems in differential equations based on the concept of a weak solution and on the lax-milgram theorem; The eigenvalue problem; Some special methods. Regularity of the weak solution.
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Nonlinear Functional Analysis and its Application III

The book contains a detailed physical motivation of the relevant basic equations and a discussion of particular problems which have played a significant role in the development of physics and through which important mathematical and ...

Author: Eberhard Zeidler

Publisher:

ISBN: 354090915X

Category: Mathematics

Page: 662

View: 225

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The fourth of a five-volume exposition of the main principles of nonlinear functional analysis and its applications to the natural sciences, economics, and numerical analysis. The presentation is self-contained and accessible to the non-specialist, and topics covered include applications to mechanics, elasticity, plasticity, hydrodynamics, thermodynamics, statistical physics, and special and general relativity including cosmology. The book contains a detailed physical motivation of the relevant basic equations and a discussion of particular problems which have played a significant role in the development of physics and through which important mathematical and physical insight may be gained. It combines classical and modern ideas to build a bridge between the language and thoughts of physicists and mathematicians. Many exercises and a comprehensive bibliography complement the text.
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Equilibrium Problems Nonsmooth Optimization and Variational Inequality Models

The aim of the book is to cover the three fundamental aspects of research in equilibrium problems: the statement problem and its formulation using mainly variational methods, its theoretical solution by means of classical and new ...

Author: F. Giannessi

Publisher: Springer Science & Business Media

ISBN: 9780306480263

Category: Mathematics

Page: 304

View: 506

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The aim of the book is to cover the three fundamental aspects of research in equilibrium problems: the statement problem and its formulation using mainly variational methods, its theoretical solution by means of classical and new variational tools, the calculus of solutions and applications in concrete cases. The book shows how many equilibrium problems follow a general law (the so-called user equilibrium condition). Such law allows us to express the problem in terms of variational inequalities. Variational inequalities provide a powerful methodology, by which existence and calculation of the solution can be obtained.
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Methods of Functional Analysis for Application in Solid Mechanics

In particular, the increasingly important role of variational methods and methods
of optimization in Solid Mechanics is a tendency to be widely observed. The
origins of the calculus of variations can be found in the field of Mechanics,
especially ...

Author: J. Mason

Publisher: Elsevier

ISBN: 9781483289915

Category: Mathematics

Page: 413

View: 292

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Publications oriented to the interests of engineering scientists and graduate students on topics of functional analysis and its applications are rare - this book has been written to fill the gap in the literature. It provides a readable account of basic mathematic topics, with illustrative examples and chapters devoted to finite elements, variational principles of elasticity and plasticity, variational inequalities and elastic stability. The text is entirely self-contained and covers a wide range of topics and ideas, from elementary concepts to modern theories and applications, and includes numerous references. It is written for engineers, graduate students and researchers who need a general knowledge of modern mathematical methods in solid mechanics.
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Variational Analysis and Applications

The first half of the book (Chapters 1–6) gives a systematic exposition of key concepts and facts, containing basic material as well as some recent and new developments.

Author: Boris S. Mordukhovich

Publisher: Springer

ISBN: 9783319927756

Category: Mathematics

Page: 622

View: 272

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Building on fundamental results in variational analysis, this monograph presents new and recent developments in the field as well as selected applications. Accessible to a broad spectrum of potential readers, the main material is presented in finite-dimensional spaces. Infinite-dimensional developments are discussed at the end of each chapter with comprehensive commentaries which emphasize the essence of major results, track the genesis of ideas, provide historical comments, and illuminate challenging open questions and directions for future research. The first half of the book (Chapters 1–6) gives a systematic exposition of key concepts and facts, containing basic material as well as some recent and new developments. These first chapters are particularly accessible to masters/doctoral students taking courses in modern optimization, variational analysis, applied analysis, variational inequalities, and variational methods. The reader’s development of skills will be facilitated as they work through each, or a portion of, the multitude of exercises of varying levels. Additionally, the reader may find hints and references to more difficult exercises and are encouraged to receive further inspiration from the gems in chapter commentaries. Chapters 7–10 focus on recent results and applications of variational analysis to advanced problems in modern optimization theory, including its hierarchical and multiobjective aspects, as well as microeconomics, and related areas. It will be of great use to researchers and professionals in applied and behavioral sciences and engineering.
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Variational Analysis and Set Optimization

This book contains the latest advances in variational analysis and set / vector optimization, including uncertain optimization, optimal control and bilevel optimization.

Author: Akhtar A. Khan

Publisher: CRC Press

ISBN: 9781351712064

Category: Business & Economics

Page: 324

View: 656

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This book contains the latest advances in variational analysis and set / vector optimization, including uncertain optimization, optimal control and bilevel optimization. Recent developments concerning scalarization techniques, necessary and sufficient optimality conditions and duality statements are given. New numerical methods for efficiently solving set optimization problems are provided. Moreover, applications in economics, finance and risk theory are discussed. Summary The objective of this book is to present advances in different areas of variational analysis and set optimization, especially uncertain optimization, optimal control and bilevel optimization. Uncertain optimization problems will be approached from both a stochastic as well as a robust point of view. This leads to different interpretations of the solutions, which widens the choices for a decision-maker given his preferences. Recent developments regarding linear and nonlinear scalarization techniques with solid and nonsolid ordering cones for solving set optimization problems are discussed in this book. These results are useful for deriving optimality conditions for set and vector optimization problems. Consequently, necessary and sufficient optimality conditions are presented within this book, both in terms of scalarization as well as generalized derivatives. Moreover, an overview of existing duality statements and new duality assertions is given. The book also addresses the field of variable domination structures in vector and set optimization. Including variable ordering cones is especially important in applications such as medical image registration with uncertainties. This book covers a wide range of applications of set optimization. These range from finance, investment, insurance, control theory, economics to risk theory. As uncertain multi-objective optimization, especially robust approaches, lead to set optimization, one main focus of this book is uncertain optimization. Important recent developments concerning numerical methods for solving set optimization problems sufficiently fast are main features of this book. These are illustrated by various examples as well as easy-to-follow-steps in order to facilitate the decision process for users. Simple techniques aimed at practitioners working in the fields of mathematical programming, finance and portfolio selection are presented. These will help in the decision-making process, as well as give an overview of nondominated solutions to choose from.
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Theory and Techniques of Optimization for Practicing Engineers

1 INTRODUCTION The classification of methods used in this section has been
suggested by several authors . Further discussion on the ... Denn , Morton M .
Optimization by Variational Methods , McGraw - Hill Book Co . , New York , 1969 .
4 .

Author: Raymond L. Zahradnik

Publisher:

ISBN: UCSD:31822014172704

Category: Mathematical optimization

Page: 326

View: 768

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An Introduction to Modern Variational Techniques in Mechanics and Engineering

* Atanackovic has good track record with Birkhauser: his "Theory of Elasticity" book (4072-X) has been well reviewed. * Current text has received two excellent pre-pub reviews. * May be used as textbook in advanced undergrad/beginning grad ...

Author: Bozidar D. Vujanovic

Publisher: Springer Science & Business Media

ISBN: 0817633995

Category: Mathematics

Page: 346

View: 635

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* Atanackovic has good track record with Birkhauser: his "Theory of Elasticity" book (4072-X) has been well reviewed. * Current text has received two excellent pre-pub reviews. * May be used as textbook in advanced undergrad/beginning grad advanced dynamics courses in engineering, physics, applied math departments. *Also useful as self-study reference for researchers and practitioners. * Many examples and novel applications throughout. Competitive literature---Meirovich, Goldstein---is outdated and does not include the synthesis of topics presented here.
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Applied Mechanics Reviews

... ( D.R.J. ) , ( et al . ) , 10752 finite element techniques , boundary value
problems , inequalities , variational methods , Hlavacek ( 1. ) , 43 • nonlinear
programming , numerical methods , optimization , structural analysis , Felippa (
C.A. ) , 44 ...

Author:

Publisher:

ISBN: OSU:32435026161059

Category: Mechanics, Applied

Page:

View: 826

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Newton Type Methods for Optimization and Variational Problems

This book presents comprehensive state-of-the-art theoretical analysis of the fundamental Newtonian and Newtonian-related approaches to solving optimization and variational problems.

Author: Alexey F. Izmailov

Publisher: Springer

ISBN: 9783319042473

Category: Business & Economics

Page: 573

View: 557

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This book presents comprehensive state-of-the-art theoretical analysis of the fundamental Newtonian and Newtonian-related approaches to solving optimization and variational problems. A central focus is the relationship between the basic Newton scheme for a given problem and algorithms that also enjoy fast local convergence. The authors develop general perturbed Newtonian frameworks that preserve fast convergence and consider specific algorithms as particular cases within those frameworks, i.e., as perturbations of the associated basic Newton iterations. This approach yields a set of tools for the unified treatment of various algorithms, including some not of the Newton type per se. Among the new subjects addressed is the class of degenerate problems. In particular, the phenomenon of attraction of Newton iterates to critical Lagrange multipliers and its consequences as well as stabilized Newton methods for variational problems and stabilized sequential quadratic programming for optimization. This volume will be useful to researchers and graduate students in the fields of optimization and variational analysis.
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