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| Author | : Pshenichnyi |
| Publisher | : CRC Press |
| Total Pages | : 258 |
| Release | : 1971-05-01 |
| Genre | : Mathematics |
| ISBN | : 9780824715564 |
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.
| Author | : B.N. Pshenichnyi |
| Publisher | : CRC Press |
| Total Pages | : 252 |
| Release | : 2020-08-18 |
| Genre | : Mathematics |
| ISBN | : 1000148696 |
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.
| Author | : I. M. Gelfand |
| Publisher | : Courier Corporation |
| Total Pages | : 260 |
| Release | : 2012-04-26 |
| Genre | : Mathematics |
| ISBN | : 0486135012 |
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.
| Author | : Mordecai Avriel |
| Publisher | : Courier Corporation |
| Total Pages | : 548 |
| Release | : 2003-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780486432274 |
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.
| Author | : Georgiĭ Aleksandrovich Kamenskiĭ |
| Publisher | : Nova Publishers |
| Total Pages | : 242 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 9781600215643 |
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.
| Author | : Yury Shestopalov |
| Publisher | : Cambridge Scholars Publishing |
| Total Pages | : 261 |
| Release | : 2023-08-09 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 1527528812 |
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.
| Author | : I. V. Girsanov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 142 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642806848 |
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.
| Author | : |
| Publisher | : Elsevier |
| Total Pages | : 473 |
| Release | : 2009-06-15 |
| Genre | : Mathematics |
| ISBN | : 0080875270 |
Theory of Extremal Problems
| Author | : Boris Nikolaevich Pshenichnyi |
| Publisher | : |
| Total Pages | : 230 |
| Release | : 1971 |
| Genre | : |
| ISBN | : |
| Author | : Delia Koo |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 229 |
| Release | : 2013-11-11 |
| Genre | : Science |
| ISBN | : 1461263581 |
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.
