Books in Calculus of variations and optimal control optimization

11-20 of 21 results in All results

Control and Optimal Control Theories with Applications

• 1st Edition
• December 1, 2004
• D N Burghes + 1 more
• English
• eBook 978-0-85709-949-5

  9 7 8 - 0 - 8 5 7 0 9 - 9 4 9 - 5

This sound introduction to classical and modern control theory concentrates on fundamental concepts. Employing the minimum of mathematical elaboration, it investigates the many applications of control theory to varied and important present-day problems, e.g. economic growth, resource depletion, disease epidemics, exploited population, and rocket trajectories. An original feature is the amount of space devoted to the important and fascinating subject of optimal control. The work is divided into two parts. Part one deals with the control of linear time-continuous systems, using both transfer function and state-space methods. The ideas of controllability, observability and minimality are discussed in comprehensible fashion. Part two introduces the calculus of variations, followed by analysis of continuous optimal control problems. Each topic is individually introduced and carefully explained with illustrative examples and exercises at the end of each chapter to help and test the reader’s understanding. Solutions are provided at the end of the book.

Mathematics of Optimization: Smooth and Nonsmooth Case

• 1st Edition
• March 10, 2004
• Giorgio Giorgi + 2 more
• English
• eBook 978-0-08-053595-1

  9 7 8 - 0 - 0 8 - 0 5 3 5 9 5 - 1

The book is intended for people (graduates, researchers, but also undergraduates with a good mathematical background) involved in the study of (static) optimization problems (in finite-dimensional spaces). It contains a lot of material, from basic tools of convex analysis to optimality conditions for smooth optimization problems, for non smooth optimization problems and for vector optimization problems.The development of the subjects are self-contained and the bibliographical references are usually treated in different books (only a few books on optimization theory deal also with vector problems), so the book can be a starting point for further readings in a more specialized literature.Assuming only a good (even if not advanced) knowledge of mathematical analysis and linear algebra, this book presents various aspects of the mathematical theory in optimization problems. The treatment is performed in finite-dimensional spaces and with no regard to algorithmic questions. After two chapters concerning, respectively, introductory subjects and basic tools and concepts of convex analysis, the book treats extensively mathematical programming problems in the smmoth case, in the nonsmooth case and finally vector optimization problems.

Networks and Graphs

• 1st Edition
• January 1, 2003
• D K Smith
• English
• Hardback 978-1-898563-91-4

  9 7 8 - 1 - 8 9 8 5 6 3 - 9 1 - 4
• eBook 978-0-85709-957-0

  9 7 8 - 0 - 8 5 7 0 9 - 9 5 7 - 0

Dr Smith here presents essential mathematical and computational ideas of network optimisation for senior undergraduate and postgraduate students in mathematics, computer science and operational research. He shows how algorithms can be used for finding optimal paths and flows, identifying trees in networks, and optimal matching. Later chapters discuss postman and salesperson tours, and demonstrate how many network problems are related to the ‘‘minimal-cost feasible-flow’’ problem. Techniques are presented both informally and with mathematical rigour and aspects of computation, especially of complexity, have been included. Numerous examples and diagrams illustrate the techniques and applications. The book also includes problem exercises with tutorial hints.

Inherently Parallel Algorithms in Feasibility and Optimization and their Applications

• 1st Edition
• Volume 8
• June 18, 2001
• D. Butnariu + 2 more
• English
• eBook 978-0-08-050876-4

  9 7 8 - 0 - 0 8 - 0 5 0 8 7 6 - 4

The Haifa 2000 Workshop on "Inherently Parallel Algorithms for Feasibility and Optimization and their Applications" brought together top scientists in this area. The objective of the Workshop was to discuss, analyze and compare the latest developments in this fast growing field of applied mathematics and to identify topics of research which are of special interest for industrial applications and for further theoretical study.Inherently parallel algorithms, that is, computational methods which are, by their mathematical nature, parallel, have been studied in various contexts for more than fifty years. However, it was only during the last decade that they have mostly proved their practical usefulness because new generations of computers made their implementation possible in order to solve complex feasibility and optimization problems involving huge amounts of data via parallel processing. These led to an accumulation of computational experience and theoretical information and opened new and challenging questions concerning the behavior of inherently parallel algorithms for feasibility and optimization, their convergence in new environments and in circumstances in which they were not considered before their stability and reliability. Several research groups all over the world focused on these questions and it was the general feeling among scientists involved in this effort that the time has come to survey the latest progress and convey a perspective for further development and concerted scientific investigations. Thus, the editors of this volume, with the support of the Israeli Academy for Sciences and Humanities, took the initiative of organizing a Workshop intended to bring together the leading scientists in the field. The current volume is the Proceedings of the Workshop representing the discussions, debates and communications that took place. Having all that information collected in a single book will provide mathematicians and engineers interested in the theoretical and practical aspects of the inherently parallel algorithms for feasibility and optimization with a tool for determining when, where and which algorithms in this class are fit for solving specific problems, how reliable they are, how they behave and how efficient they were in previous applications. Such a tool will allow software creators to choose ways of better implementing these methods by learning from existing experience.

Nonlinear Equations and Optimisation

• 1st Edition
• Volume 4
• March 14, 2001
• L.T. Watson + 2 more
• English
• eBook 978-0-08-092954-5

  9 7 8 - 0 - 0 8 - 0 9 2 9 5 4 - 5

/homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price !In one of the papers in this collection, the remark that "nothing at all takes place in the universe in which some rule of maximum of minimum does not appear" is attributed to no less an authority than Euler. Simplifying the syntax a little, we might paraphrase this as Everything is an optimization problem. While this might be something of an overstatement, the element of exaggeration is certainly reduced if we consider the extended form: Everything is an optimization problem or a system of equations. This observation, even if only partly true, stands as a fitting testimonial to the importance of the work covered by this volume.Since the 1960s, much effort has gone into the development and application of numerical algorithms for solving problems in the two areas of optimization and systems of equations. As a result, many different ideas have been proposed for dealing efficiently with (for example) severe nonlinearities and/or very large numbers of variables. Libraries of powerful software now embody the most successful of these ideas, and one objective of this volume is to assist potential users in choosing appropriate software for the problems they need to solve. More generally, however, these collected review articles are intended to provide both researchers and practitioners with snapshots of the 'state-of-the-art' with regard to algorithms for particular classes of problem. These snapshots are meant to have the virtues of immediacy through the inclusion of very recent ideas, but they also have sufficient depth of field to show how ideas have developed and how today's research questions have grown out of previous solution attempts.The most efficient methods for local optimization, both unconstrained and constrained, are still derived from the classical Newton approach.As well as dealing in depth with the various classical, or neo-classical, approaches, the selection of papers on optimization in this volume ensures that newer ideas are also well represented.Solving nonlinear algebraic systems of equations is closely related to optimization. The two are not completely equivalent, however, and usually something is lost in the translation.Algorithms for nonlinear equations can be roughly classified as locally convergent or globally convergent. The characterization is not perfect.Locally convergent algorithms include Newton's method, modern quasi-Newton variants of Newton's method, and trust region methods. All of these approaches are well represented in this volume.

Introduction to Global Variational Geometry

• 1st Edition
• Volume 16
• April 1, 2000
• Demeter Krupka
• English
• eBook 978-0-08-095423-3

  9 7 8 - 0 - 0 8 - 0 9 5 4 2 3 - 3

This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field. Featured topics- Analysis on manifolds- Differential forms on jet spaces - Global variational functionals- Euler-Lagrange mapping - Helmholtz form and the inverse problem- Symmetries and the Noether’s theory of conservation laws- Regularity and the Hamilton theory- Variational sequences - Differential invariants and natural variational principles

Introduction to Global Variational Geometry

• 1st Edition
• Volume 20
• April 1, 2000
• Demeter Krupka
• English
• eBook 978-0-08-095427-1

  9 7 8 - 0 - 0 8 - 0 9 5 4 2 7 - 1

This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field. Featured topics- Analysis on manifolds- Differential forms on jet spaces - Global variational functionals- Euler-Lagrange mapping - Helmholtz form and the inverse problem- Symmetries and the Noether’s theory of conservation laws- Regularity and the Hamilton theory- Variational sequences - Differential invariants and natural variational principles

Introduction to Global Variational Geometry

• 1st Edition
• Volume 10
• April 1, 2000
• Demeter Krupka
• English
• eBook 978-0-08-095418-9

  9 7 8 - 0 - 0 8 - 0 9 5 4 1 8 - 9

This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field. Featured topics- Analysis on manifolds- Differential forms on jet spaces - Global variational functionals- Euler-Lagrange mapping - Helmholtz form and the inverse problem- Symmetries and the Noether’s theory of conservation laws- Regularity and the Hamilton theory- Variational sequences - Differential invariants and natural variational principles

Variational Methods in Nonconservative Phenomena

• 1st Edition
• Volume 182
• May 1, 1989
• B. D. Vujanovic + 1 more
• English
• eBook 978-0-08-092642-1

  9 7 8 - 0 - 0 8 - 0 9 2 6 4 2 - 1

This book provides a comprehensive survey of analytic and approximate solutions of problems of applied mechanics, with particular emphasis on nonconservative phenomena. Include

Mathematical Physics

• 1st Edition
• Volume 152
• June 1, 1988
• R. Carroll
• English
• eBook 978-0-08-087263-6

  9 7 8 - 0 - 0 8 - 0 8 7 2 6 3 - 6

An introduction to the important areas of mathematical physics, this volume starts with basic ideas and proceeds (sometimes rapidly) to a more sophisticated level, often to the context of current research.All of the necessary functional analysis and differential geometry is included, along with basic calculus of variations and partial differential equations (linear and nonlinear). An introduction to classical and quantum mechanics is given with topics in Feynman integrals, gauge fields, geometric quantization, attractors for PDE, Ginzburg-Landau Equations in superconductivity, Navier-Stokes equations, soliton theory, inverse problems and ill-posed problems, scattering theory, convex analysis, variational inequalities, nonlinear semigroups, etc. Contents: 1. Classical Ideas and Problems. Introduction. Some Preliminary Variational Ideas. Various Differential Equations and Their Origins. Linear Second Order PDE. Further Topics in the Calculus of Variations. Spectral Theory for Ordinary Differential Operators, Transmutation, and Inverse Problems. Introduction to Classical Mechanics. Introduction to Quantum Mechanics. Weak Problems in PDE. Some Nonlinear PDE. Ill-Posed Problems and Regularization. 2. Scattering Theory and Solitons. Introduction. Scattering Theory I (Operator Theory). Scattering Theory II (3-D). Scattering Theory III (A Medley of Themes). Scattering Theory IV (Spectral Methods in 3-D). Systems and Half Line Problems. Relations between Potentials and Spectral Data. Introduction to Soliton Theory. Solitons via AKNS Systems. Soliton Theory (Hamiltonian Structure). Some Topics in Integrable Systems. 3. Some Nonlinear Analysis: Some Geometric Formalism. Introduction. Nonlinear Analysis. Monotone Operators. Topological Methods. Convex Analysis. Nonlinear Semigroups and Monotone Sets. Variational Inequalities. Quantum Field Theory. Gauge Fields (Physics). Gauge Fields (Mathematics) and Geometric Quantization. Appendices: Introduction to Linear Functional Analysis. Selected Topics in Functional Analysis. Introduction to Differential Geometry. References. Index.