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Author: I. Bert Russak
Publisher:
Published: 1973
Total Pages: 34
ISBN-13:
DOWNLOAD EBOOKA set of second order necessary conditions is obtained for solution to a basic problem in optimal control involving the state constraints psi sup alpha (t, x)
Author: Ira Bert Russak
Publisher:
Published: 1973
Total Pages: 0
ISBN-13:
DOWNLOAD EBOOKThe paper is a sequel to an article by the author, concerned with a certain canonical problem in optimal control involving constraints of the type (Psi sup alpha) (t, x) or = 0 alpha = 1 ..., m. In that article a set of second order conditions necessary for a solution arc was obtained. In the paper those results are extended to a general control problem involving the above type of constraints. (Author).
Author: Aram Arutyunov
Publisher: Springer Science & Business Media
Published: 2000-10-31
Total Pages: 318
ISBN-13: 9780792366553
DOWNLOAD EBOOKThis book is devoted to one of the main questions of the theory of extremal problems, namely, to necessary and sufficient extremality conditions. The book consists of four parts. First, the abstract minimization problem with constraints is studied. The next chapter is devoted to one of the most important classes of extremal problems, the optimal control problem. Next, one of the main objects of the calculus of variations is studied, the integral quadratic form. Finally, local properties of smooth nonlinear mappings in a neighborhood of an abnormal point will be discussed. Audience: The book is intended for researchers interested in optimization problems. The book may also be useful for advanced students and postgraduate students.
Author: Daniel Liberzon
Publisher: Princeton University Press
Published: 2012
Total Pages: 255
ISBN-13: 0691151873
DOWNLOAD EBOOKThis 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: Jasbir Singh Arora
Publisher: Academic Press
Published: 2011-08-12
Total Pages: 897
ISBN-13: 012381376X
DOWNLOAD EBOOKIntroduction to Optimum Design, Third Edition describes an organized approach to engineering design optimization in a rigorous yet simplified manner. It illustrates various concepts and procedures with simple examples and demonstrates their applicability to engineering design problems. Formulation of a design problem as an optimization problem is emphasized and illustrated throughout the text. Excel and MATLAB® are featured as learning and teaching aids. Basic concepts of optimality conditions and numerical methods are described with simple and practical examples, making the material highly teachable and learnable Includes applications of optimization methods for structural, mechanical, aerospace, and industrial engineering problems Introduction to MATLAB Optimization Toolbox Practical design examples introduce students to the use of optimization methods early in the book New example problems throughout the text are enhanced with detailed illustrations Optimum design with Excel Solver has been expanded into a full chapter New chapter on several advanced optimum design topics serves the needs of instructors who teach more advanced courses
Author: Xin-She Yang
Publisher: Academic Press
Published: 2019-06-17
Total Pages: 188
ISBN-13: 0128172177
DOWNLOAD EBOOKIntroduction to Algorithms for Data Mining and Machine Learning introduces the essential ideas behind all key algorithms and techniques for data mining and machine learning, along with optimization techniques. Its strong formal mathematical approach, well selected examples, and practical software recommendations help readers develop confidence in their data modeling skills so they can process and interpret data for classification, clustering, curve-fitting and predictions. Masterfully balancing theory and practice, it is especially useful for those who need relevant, well explained, but not rigorous (proofs based) background theory and clear guidelines for working with big data. Presents an informal, theorem-free approach with concise, compact coverage of all fundamental topics Includes worked examples that help users increase confidence in their understanding of key algorithms, thus encouraging self-study Provides algorithms and techniques that can be implemented in any programming language, with each chapter including notes about relevant software packages
Author: J Gregory
Publisher: CRC Press
Published: 2018-01-18
Total Pages: 218
ISBN-13: 1351087762
DOWNLOAD EBOOKThe 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: Garth P. McCormick
Publisher:
Published: 1967
Total Pages: 23
ISBN-13:
DOWNLOAD EBOOKThis paper establishes two sets of 'second-order' conditions--one that is necessary, and the other that is sufficient that a vector chi* be a local minimum to the constrained optimization problem: minimize f(chi) subject to the constraints g sub i(chi) = or> 0, i = 1, ..., m, and h sub j(chi) = 0, j=1, ..., p where the problem functions are twice continuously differentiable. The necessary conditions extend the well-known results obtained with Lagrange multipliers that apply to equality-constrained optimization problems, and the Kuhn-Tucker conditions that apply to mixed inequality and equality problems when the problem functions are required only to have continuous first derivatives. The sufficient conditions extend similar conditions that have been developed only for equality-constrained problems. Examples of the applications of these sets of conditions are given. (Author).
Author: Amir Beck
Publisher: SIAM
Published: 2014-10-27
Total Pages: 286
ISBN-13: 1611973651
DOWNLOAD EBOOKThis 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.
Author: Gershon Wolansky
Publisher: American Mathematical Soc.
Published: 2014-07-01
Total Pages: 266
ISBN-13: 147041077X
DOWNLOAD EBOOKThis volume contains the proceedings of the workshop on Variational and Optimal Control Problems on Unbounded Domains, held in memory of Arie Leizarowitz, from January 9-12, 2012, in Haifa, Israel. The workshop brought together a select group of worldwide experts in optimal control theory and the calculus of variations, working on problems on unbounded domains. The papers in this volume cover many different areas of optimal control and its applications. Topics include needle variations in infinite-horizon optimal control, Lyapunov stability with some extensions, small noise large time asymptotics for the normalized Feynman-Kac semigroup, linear-quadratic optimal control problems with state delays, time-optimal control of wafer stage positioning, second order optimality conditions in optimal control, state and time transformations of infinite horizon problems, turnpike properties of dynamic zero-sum games, and an infinite-horizon variational problem on an infinite strip. This book is co-published with Bar-Ilan University (Ramat-Gan, Israel).
