Download or read book Necessary Conditions for an Extremum written by Pshenichnyi and published by CRC Press. This book was released on 1971-05-01 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a theory of necessary conditions for an extremum, including formal conditions for an extremum and computational methods. It states the general results of the theory and shows how these results can be particularized to specific problems.
Download or read book Calculus of Variations written by I. M. Gelfand and published by Courier Corporation. This book was released on 2012-04-26 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fresh, lively text serves as a modern introduction to the subject, with applications to the mechanics of systems with a finite number of degrees of freedom. Ideal for math and physics students.
Download or read book Necessary Conditions for an Extremum written by B.N. Pshenichnyi and published by CRC Press. This book was released on 2020-08-18 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a theory of necessary conditions for an extremum, including formal conditions for an extremum and computational methods. It states the general results of the theory and shows how these results can be particularized to specific problems.
Download or read book Nonlinear Programming written by Mordecai Avriel and published by Courier Corporation. This book was released on 2003-01-01 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: This overview provides a single-volume treatment of key algorithms and theories. Begins with the derivation of optimality conditions and discussions of convex programming, duality, generalized convexity, and analysis of selected nonlinear programs, and then explores techniques for numerical solutions and unconstrained optimization methods. 1976 edition. Includes 58 figures and 7 tables.
Download or read book Extrema of Nonlocal Functionals and Boundary Value Problems for Functional Differential Equations written by Georgiĭ Aleksandrovich Kamenskiĭ and published by Nova Publishers. This book was released on 2007 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: The non-local functional is an integral with the integrand depending on the unknown function at different values of the argument. These types of functionals have different applications in physics, engineering and sciences. The Euler type equations that arise as necessary conditions of extrema of non-local functionals are the functional differential equations. The book is dedicated to systematic study of variational calculus for non-local functionals and to theory of boundary value problems for functional differential equations. There are described different necessary and some sufficient conditions for extrema of non-local functionals. Theorems of existence and uniqueness of solutions to many kinds of boundary value problems for functional differential equations are proved. The spaces of solutions to these problems are, as a rule, Sobolev spaces and it is not often possible to apply the analytical methods for solution of these problems. Therefore it is important to have approximate methods for their solution. Different approximate methods of solution of boundary value problems for functional differential equations and direct methods of variational calculus for non-local functionals are described in the book. The non-local functional is an integral with the integrand depending on the unknown function at different values of the argument. These types of functionals have different applications in physics, engineering and sciences. The Euler type equations that arise as necessary conditions of extrema of non-local functionals are the functional differential equations. The book is dedicated to systematic study of variational calculus for non-local functionals and to theory of boundary value problems for functional differential equations. There are described different necessary and some sufficient conditions for extrema of non-local functionals. Theorems of existence and uniqueness of solutions to many kinds of boundary value problems for functional differential equations are proved. The spaces of solutions to these problems are, as a rule, Sobolev spaces and it is not often possible to apply the analytical methods for solution of these problems. Therefore it is important to have approximate methods for their solution. Different approximate methods of solution of boundary value problems for functional differential equations and direct methods of variational calculus for non-local functionals are described in the book.
Download or read book An Introduction to Optimal Control written by Yury Shestopalov and published by Cambridge Scholars Publishing. This book was released on 2023-08-09 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the major techniques involved in optimization, control theory, and calculus of variations. The book serves as a concise contemporary guide to optimal control theory, optimization, numerical methods and beyond. As such, it is a valuable source to learn mathematical modeling and the mathematical nature of optimization and optimal control. The presence of a variety of exercises solved down to numerical values is one of the main characteristic features of the book. Another one is its compactness, and the material’s usefulness in preparing and teaching several different university courses. The investigation of trends and their formation undertaken in the book leads seamlessly into extrapolation techniques and rigorous methods of scientific prediction. The research for this book was accomplished at the Russian Technological University (RTU) MIREA, based on the courses which have been taught at the RTU for many years.
Download or read book Lectures on Mathematical Theory of Extremum Problems written by I. V. Girsanov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author of this book, Igor' Vladimirovich Girsanov, was one of the first mathematicians to study general extremum problems and to realize the feasibility and desirability of a unified theory of extremal problems, based on a functional analytic approach. He actively advocated this view, and his special course, given at the Faculty of Mechanics and Mathematics of the Moscow State University in 1963 and 1964, was apparently the first systematic exposition of a unified approach to the theory of extremal problems. This approach was based on the ideas of Dubovitskii and Milyutin [1]. The general theory of extremal problems has developed so intensely during the past few years that its basic concepts may now be considered finalized. Nevertheless, as yet the basic results of this new field of mathematics have not been presented in a form accessible to a wide range of readers. (The profound paper of Dubovitskii and Milyutin [2] can hardly be recommended for a first study of the theory, since, in particular, it does not contain proofs of the fundamental theorems. ) Girsanov's book fills this gap. It contains a systematic exposition of the general principles underlying the derivation of necessary and sufficient conditions for an extremum, in a wide variety of problems. Numerous applications are given to specific extremal problems. The main material is preceded by an introductory section in which all prerequisites from functional analysis are presented.
Download or read book Theory of Extremal Problems written by and published by Elsevier. This book was released on 2009-06-15 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory of Extremal Problems
Download or read book Necessary Conditions for an Extremum written by Boris Nikolaevich Pshenichnyi and published by . This book was released on 1971 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Optimality Conditions Abnormal and Degenerate Problems written by Aram Arutyunov and published by Springer Science & Business Media. This book was released on 2000-10-31 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 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.
Download or read book Elements of Optimization written by Delia Koo and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book attempts to present the concepts which underlie the various optimization procedures which are commonly used. It is written primarily for those scientists such as economists, operations researchers, and en gineers whose main tools of analysis involve optimization techniques and who possess a (not very sharp) knowledge of one or one-and-a-half year's calculus through partial differentiation and Taylor's theorem and some acquaintance with elementary vector and matrix terminology. Such a scientist is frequently confronted with expressions such as Lagrange multi pliers, first-and second-order conditions, linear programming and activity analysis, duality, the Kuhn-Tucker conditions, and, more recently, dy namic programming and optimal control. He or she uses or needs to use these optimization techniques, and would like to feel more comfortable with them through better understanding of their underlying mathematical concepts, but has no immediate use for a formal theorem-proof treatment which quickly abstracts to a general case of n variables and uses a style and terminology that are discouraging to people who are not mathematics majors. The emphasis of this book is on clarity and plausibility. Through examples which are worked out step by step in detail, I hope to illustrate some tools which will be useful to scientists when they apply optimization techniques to their problems. Most of the chapters may be read independently of each other-with the exception of Chapter 6, which depends on Chapter 5. For instance, the reader will find little or no difficulty in reading Chapter 8 without having read the previous chapters.
Download or read book Foundations of Theoretical Mechanics I written by Ruggero Maria Santilli and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The objective of this monograph is to present some methodological foundations of theoretical mechanics that are recommendable to graduate students prior to, or jointly with, the study of more advanced topics such as statistical mechanics, thermodynamics, and elementary particle physics. A program of this nature is inevitably centered on the methodological foundations for Newtonian systems, with particular reference to the central equations of our theories, that is, Lagrange's and Hamilton's equations. This program, realized through a study of the analytic representations in terms of Lagrange's and Hamilton's equations of generally nonconservative Newtonian systems (namely, systems with Newtonian forces not necessarily derivable from a potential function), falls within the context of the so-called Inverse Problem, and consists of three major aspects: l. The study of the necessary and sufficient conditions for the existence of a Lagrangian or Hamiltonian representation of given equations of motion with arbitrary forces; 2. The identification of the methods for the construction of a Lagrangian or Hamiltonian from given equations of motion verifying conditions 1; and 3 The analysis of the significance of the underlying methodology for other aspects of Newtonian Mechanics, e. g. , transformation theory, symmetries, and first integrals for nonconservative Newtonian systems. This first volume is devoted to the foundations of the Inverse Problem, with particular reference to aspects I and 2.
Download or read book Optimal Control written by V. M. Alekseev and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is an ever-growing interest in control problems today, con nected with the urgent problems of the effective use of natural resources, manpower, materials, and technology. When referring to the most important achievements of science and technology in the 20th Century, one usually mentions the splitting of the atom, the exploration of space, and computer engineering. Achievements in control theory seem less spectacular when viewed against this background, but the applications of control theory are playing an important role in the development of modern civilization, and there is every reason to believe that this role will be even more signifi cant in the future. Wherever there is active human participation, the problem arises of finding the best, or optimal, means of control. The demands of economics and technology have given birth to optimization problems which, in turn, have created new branches of mathematics. In the Forties, the investigation of problems of economics gave rise to a new branch of mathematical analysis called linear and convex program ming. At that time, problems of controlling flying vehicles and technolog ical processes of complex structures became important. A mathematical theory was formulated in the mid-Fifties known as optimal control theory. Here the maximum principle of L. S. Pontryagin played a pivotal role. Op timal control theory synthesized the concepts and methods of investigation using the classical methods of the calculus of variations and the methods of contemporary mathematics, for which Soviet mathematicians made valuable contributions.
Download or read book Encyclopedia of Optimization written by Christodoulos A. Floudas and published by Springer Science & Business Media. This book was released on 2008-09-04 with total page 4646 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".
Download or read book Fundamentals of Structural Mechanics written by Keith D. Hjelmstad and published by Springer Science & Business Media. This book was released on 2004-11-12 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: A solid introduction to basic continuum mechanics, emphasizing variational formulations and numeric computation. The book offers a complete discussion of numerical method techniques used in the study of structural mechanics.
Download or read book Calculus of Variations and Optimal Control Theory written by Daniel Liberzon and published by Princeton University Press. This book was released on 2012 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Fundamental Theories and Their Applications of the Calculus of Variations written by Dazhong Lao and published by Springer Nature. This book was released on 2020-09-02 with total page 1006 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the calculus of variations, including fundamental theories and applications. This textbook is intended for graduate and higher-level college and university students, introducing them to the basic concepts and calculation methods used in the calculus of variations. It covers the preliminaries, variational problems with fixed boundaries, sufficient conditions of extrema of functionals, problems with undetermined boundaries, variational problems of conditional extrema, variational problems in parametric forms, variational principles, direct methods for variational problems, variational principles in mechanics and their applications, and variational problems of functionals with vector, tensor and Hamiltonian operators. Many of the contributions are based on the authors’ research, addressing topics such as the extension of the connotation of the Hilbert adjoint operator, definitions of the other three kinds of adjoint operators, the extremum function theorem of the complete functional, unified Euler equations in variational methods, variational theories of functionals with vectors, modulus of vectors, arbitrary order tensors, Hamiltonian operators and Hamiltonian operator strings, reconciling the Euler equations and the natural boundary conditions, and the application range of variational methods. The book is also a valuable reference resource for teachers as well as science and technology professionals.
