Constrained Optimization In The Calculus Of Variations And Optimal Control Theory
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| Author | : J Gregory |
| Publisher | : CRC Press |
| Total Pages | : 218 |
| Release | : 2018-01-18 |
| Genre | : Mathematics |
| ISBN | : 1351087762 |
The major purpose of this book is to present the theoretical ideas and the analytical and numerical methods to enable the reader to understand and efficiently solve these important optimizational problems.The first half of this book should serve as the major component of a classical one or two semester course in the calculus of variations and optimal control theory. The second half of the book will describe the current research of the authors which is directed to solving these problems numerically. In particular, we present new reformulations of constrained problems which leads to unconstrained problems in the calculus of variations and new general, accurate and efficient numerical methods to solve the reformulated problems. We believe that these new methods will allow the reader to solve important problems.
| Author | : J Gregory |
| Publisher | : CRC Press |
| Total Pages | : 232 |
| Release | : 2018-01-18 |
| Genre | : Mathematics |
| ISBN | : 135107931X |
The major purpose of this book is to present the theoretical ideas and the analytical and numerical methods to enable the reader to understand and efficiently solve these important optimizational problems.The first half of this book should serve as the major component of a classical one or two semester course in the calculus of variations and optimal control theory. The second half of the book will describe the current research of the authors which is directed to solving these problems numerically. In particular, we present new reformulations of constrained problems which leads to unconstrained problems in the calculus of variations and new general, accurate and efficient numerical methods to solve the reformulated problems. We believe that these new methods will allow the reader to solve important problems.
| Author | : Daniel Liberzon |
| Publisher | : Princeton University Press |
| Total Pages | : 255 |
| Release | : 2012 |
| Genre | : Mathematics |
| ISBN | : 0691151873 |
This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. Designed specifically for a one-semester course, the book begins with calculus of variations, preparing the ground for optimal control. It then gives a complete proof of the maximum principle and covers key topics such as the Hamilton-Jacobi-Bellman theory of dynamic programming and linear-quadratic optimal control. Calculus of Variations and Optimal Control Theory also traces the historical development of the subject and features numerous exercises, notes and references at the end of each chapter, and suggestions for further study. Offers a concise yet rigorous introduction Requires limited background in control theory or advanced mathematics Provides a complete proof of the maximum principle Uses consistent notation in the exposition of classical and modern topics Traces the historical development of the subject Solutions manual (available only to teachers) Leading universities that have adopted this book include: University of Illinois at Urbana-Champaign ECE 553: Optimum Control Systems Georgia Institute of Technology ECE 6553: Optimal Control and Optimization University of Pennsylvania ESE 680: Optimal Control Theory University of Notre Dame EE 60565: Optimal Control
| Author | : Morton I. Kamien |
| Publisher | : Courier Corporation |
| Total Pages | : 402 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 0486310280 |
Since its initial publication, this text has defined courses in dynamic optimization taught to economics and management science students. The two-part treatment covers the calculus of variations and optimal control. 1998 edition.
| Author | : Daniel Léonard |
| Publisher | : Cambridge University Press |
| Total Pages | : 372 |
| Release | : 1992-01-31 |
| Genre | : Business & Economics |
| ISBN | : 9780521337465 |
Optimal control theory is a technique being used increasingly by academic economists to study problems involving optimal decisions in a multi-period framework. This textbook is designed to make the difficult subject of optimal control theory easily accessible to economists while at the same time maintaining rigour. Economic intuitions are emphasized, and examples and problem sets covering a wide range of applications in economics are provided to assist in the learning process. Theorems are clearly stated and their proofs are carefully explained. The development of the text is gradual and fully integrated, beginning with simple formulations and progressing to advanced topics such as control parameters, jumps in state variables, and bounded state space. For greater economy and elegance, optimal control theory is introduced directly, without recourse to the calculus of variations. The connection with the latter and with dynamic programming is explained in a separate chapter. A second purpose of the book is to draw the parallel between optimal control theory and static optimization. Chapter 1 provides an extensive treatment of constrained and unconstrained maximization, with emphasis on economic insight and applications. Starting from basic concepts, it derives and explains important results, including the envelope theorem and the method of comparative statics. This chapter may be used for a course in static optimization. The book is largely self-contained. No previous knowledge of differential equations is required.
| Author | : J.L. Troutman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 373 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1468401580 |
The calculus of variations, whose origins can be traced to the works of Aristotle and Zenodoros, is now Ii vast repository supplying fundamental tools of exploration not only to the mathematician, but-as evidenced by current literature-also to those in most branches of science in which mathematics is applied. (Indeed, the macroscopic statements afforded by variational principles may provide the only valid mathematical formulation of many physical laws. ) As such, it retains the spirit of natural philosophy common to most mathematical investigations prior to this century. How ever, it is a discipline in which a single symbol (b) has at times been assigned almost mystical powers of operation and discernment, not readily subsumed into the formal structures of modern mathematics. And it is a field for which it is generally supposed that most questions motivating interest in the subject will probably not be answerable at the introductory level of their formulation. In earlier articles,1,2 it was shown through several examples that a complete characterization of the solution of optimization problems may be available by elementary methods, and it is the purpose of this work to explore further the convexity which underlay these individual successes in the context of a full introductory treatment of the theory of the variational calculus. The required convexity is that determined through Gateaux variations, which can be defined in any real linear space and which provide an unambiguous foundation for the theory.
| Author | : John L. Troutman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 471 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461207371 |
An introduction to the variational methods used to formulate and solve mathematical and physical problems, allowing the reader an insight into the systematic use of elementary (partial) convexity of differentiable functions in Euclidian space. By helping students directly characterize the solutions for many minimization problems, the text serves as a prelude to the field theory for sufficiency, laying as it does the groundwork for further explorations in mathematics, physics, mechanical and electrical engineering, as well as computer science.
| Author | : John Gregory |
| Publisher | : Springer |
| Total Pages | : 217 |
| Release | : 1992-05-31 |
| Genre | : Computers |
| ISBN | : 9780412742309 |
A major problem in current applied mathematics is the lack of efficient and accurate techniques to solve optimization problems in the calculus of variations and optimal control theory. This is surprising since problems occur throughout many areas of applied mathematics, engineering, physical sciences, economics, and biomedicine. For instance, these techniques are used to solve rocket trajectory problems, current flow problems in electronics manufacturing, and financial risk problems in investing. The authors have written a unique book to remedy this problem. The first half of the book contains classical material in the field, the second half unique theoretical and numerical methods for constrained problems.
| Author | : John Gregory |
| Publisher | : Springer |
| Total Pages | : 217 |
| Release | : 2012-09-17 |
| Genre | : Computers |
| ISBN | : 9789401052955 |
A major problem in current applied mathematics is the lack of efficient and accurate techniques to solve optimization problems in the calculus of variations and optimal control theory. This is surprising since problems occur throughout many areas of applied mathematics, engineering, physical sciences, economics, and biomedicine. For instance, these techniques are used to solve rocket trajectory problems, current flow problems in electronics manufacturing, and financial risk problems in investing. The authors have written a unique book to remedy this problem. The first half of the book contains classical material in the field, the second half unique theoretical and numerical methods for constrained problems.
| Author | : Francis Clarke |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 589 |
| Release | : 2013-02-06 |
| Genre | : Mathematics |
| ISBN | : 1447148207 |
Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor. This book provides a thorough introduction to functional analysis and includes many novel elements as well as the standard topics. A short course on nonsmooth analysis and geometry completes the first half of the book whilst the second half concerns the calculus of variations and optimal control. The author provides a comprehensive course on these subjects, from their inception through to the present. A notable feature is the inclusion of recent, unifying developments on regularity, multiplier rules, and the Pontryagin maximum principle, which appear here for the first time in a textbook. Other major themes include existence and Hamilton-Jacobi methods. The many substantial examples, and the more than three hundred exercises, treat such topics as viscosity solutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory. They also touch lightly upon several fields of application: mechanics, economics, resources, finance, control engineering. Functional Analysis, Calculus of Variations and Optimal Control is intended to support several different courses at the first-year or second-year graduate level, on functional analysis, on the calculus of variations and optimal control, or on some combination. For this reason, it has been organized with customization in mind. The text also has considerable value as a reference. Besides its advanced results in the calculus of variations and optimal control, its polished presentation of certain other topics (for example convex analysis, measurable selections, metric regularity, and nonsmooth analysis) will be appreciated by researchers in these and related fields.
