Download or read book Turnpike Theory for the Robinson Solow Srinivasan Model written by Alexander J. Zaslavski and published by Springer Nature. This book was released on 2021-01-04 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the study of a class of optimal control problems arising in mathematical economics, related to the Robinson–Solow–Srinivasan (RSS) model. It will be useful for researches interested in the turnpike theory, infinite horizon optimal control and their applications, and mathematical economists. The RSS is a well-known model of economic dynamics that was introduced in the 1960s and as many other models of economic dynamics, the RSS model is determined by an objective function (a utility function) and a set-valued mapping (a technology map). The set-valued map generates a dynamical system whose trajectories are under consideration and the objective function determines an optimality criterion. The goal is to find optimal trajectories of the dynamical system, using the optimality criterion. Chapter 1 discusses turnpike properties for some classes of discrete time optimal control problems. Chapter 2 present the description of the RSS model and discuss its basic properties. Infinite horizon optimal control problems, related to the RSS model are studied in Chapter 3. Turnpike properties for the RSS model are analyzed in Chapter 4. Chapter 5 studies infinite horizon optimal control problems related to the RSS model with a nonconcave utility function. Chapter 6 focuses on infinite horizon optimal control problems with nonautonomous optimality criterions. Chapter 7 contains turnpike results for a class of discrete-time optimal control problems. Chapter 8 discusses the RSS model and compares different optimality criterions. Chapter 9 is devoted to the study of the turnpike properties for the RSS model. In Chapter 10 the one-dimensional autonomous RSS model is considered and the continuous time RSS model is studied in Chapter 11.

Download or read book Turnpike Theory for the Robinson Solow Srinivasan Model written by Alexander J. Zaslavski and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the study of a class of optimal control problems arising in mathematical economics, related to the Robinson-Solow-Srinivasan (RSS) model. It will be useful for researches interested in the turnpike theory, infinite horizon optimal control and their applications, and mathematical economists. The RSS is a well-known model of economic dynamics that was introduced in the 1960s and as many other models of economic dynamics, the RSS model is determined by an objective function (a utility function) and a set-valued mapping (a technology map). The set-valued map generates a dynamical system whose trajectories are under consideration and the objective function determines an optimality criterion. The goal is to find optimal trajectories of the dynamical system, using the optimality criterion. Chapter 1 discusses turnpike properties for some classes of discrete time optimal control problems. Chapter 2 present the description of the RSS model and discuss its basic properties. Infinite horizon optimal control problems, related to the RSS model are studied in Chapter 3. Turnpike properties for the RSS model are analyzed in Chapter 4. Chapter 5 studies infinite horizon optimal control problems related to the RSS model with a nonconcave utility function. Chapter 6 focuses on infinite horizon optimal control problems with nonautonomous optimality criterions. Chapter 7 contains turnpike results for a class of discrete-time optimal control problems. Chapter 8 discusses the RSS model and compares different optimality criterions. Chapter 9 is devoted to the study of the turnpike properties for the RSS model. In Chapter 10 the one-dimensional autonomous RSS model is considered and the continuous time RSS model is studied in Chapter 11.

Download or read book Turnpike Properties in the Calculus of Variations and Optimal Control written by Alexander J. Zaslavski and published by Springer Science & Business Media. This book was released on 2006-01-27 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the recent progress on the turnpike theory. The turnpike property was discovered by Paul A. Samuelson, who applied it to problems in mathematical economics in 1949. These properties were studied for optimal trajectories of models of economic dynamics determined by convex processes. In this monograph the author, a leading expert in modern turnpike theory, presents a number of results concerning the turnpike properties in the calculus of variations and optimal control which were obtained in the last ten years. These results show that the turnpike properties form a general phenomenon which holds for various classes of variational problems and optimal control problems. The book should help to correct the misapprehension that turnpike properties are only special features of some narrow classes of convex problems of mathematical economics. Audience This book is intended for mathematicians interested in optimal control, calculus of variations, game theory and mathematical economics.

Download or read book Turnpike Theory of Continuous Time Linear Optimal Control Problems written by Alexander J. Zaslavski and published by Springer. This book was released on 2015-07-01 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Individual turnpike results are of great interest due to their numerous applications in engineering and in economic theory; in this book the study is focused on new results of turnpike phenomenon in linear optimal control problems. The book is intended for engineers as well as for mathematicians interested in the calculus of variations, optimal control and in applied functional analysis. Two large classes of problems are studied in more depth. The first class studied in Chapter 2 consists of linear control problems with periodic nonsmooth convex integrands. Chapters 3-5 consist of linear control problems with autonomous convex smooth integrands. Chapter 6 discusses a turnpike property for dynamic zero-sum games with linear constraints. Chapter 7 examines genericity results. In Chapter 8, the description of structure of variational problems with extended-valued integrands is obtained. Chapter 9 ends the exposition with a study of turnpike phenomenon for dynamic games with extended value integrands.

Download or read book Classical Turnpike Theory and the Economics of Forestry written by M. Ali Khan and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "Classical turnpike theory, as originally conceived by Samuelson, pertains to optimal growth theory over a large but infinite time horizon with given initial and terminal stocks. In this paper, we present two turnpike results in the context of the economics of forestry with given initial and terminal forest configurations. Our results depart from the general theory in that they pertain to a transitional production set which does not satisfy the assumptions of inaction and free disposal, and rely on a recently-discovered noninteriority assumption on concave (not necessarily differentiable) benefit functions that implies, and is implied by, the asymptotic convergence of good programs"--Abstract.

Download or read book Theory of Economic Growth written by Michio Morishima and published by OUP Oxford. This book was released on 1969-12-04 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory of Economic Growth

Download or read book Input output Analysis the Turnpike Theorem and Economic Development written by Robert D. Corbin and published by . This book was released on 1970 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 1930's there were major contributions to the economic theory by Keynes, Leontief, and Van Neumann. Since much of the world was in the grips of a fierce depression, Keynes' timely General Theory became the much discussed economic controversy, as economics came to realize what everyone else knew too well, that unemployment could exist. During this period, the works of Leontief and von Neumann went relatively unknown. As economists became familiar with "Keynesian Economics," as interpreted by Hansen, the broad macro-model became a guide to government monetary and fiscal policy. However, Leontief continued to disaggregate these macro-models by dividing the economy into various industries and tracing thought the network of inputs and outputs. The early 1950's witnessed to Leontief publications out of the Harvard Research Project, and by now von Neumanns' article had been translated. Further, George Dantzig had developed the simplex method to solve linear programming, and electronic computers were rapidly developing to solve both the Leontief input-output and linear programming problems. Then in 1958, Dorfman, Samuelson, and Solow published their work on linear programming . These historical events lead to the topics of this paper. Many of the seemingly unrelated topics are brought together in a unified treatment, with a focus on the application of input-output analysis to develpment. Unfortunately the mathematical nature of the material has often presented a barrier to the prospective student. It is hoped that the present work will help bridge this gap.

Download or read book Weiterbildungsnormen der rztekammern auf dem rechtlichen Pr fstand written by Gunther Schwerdtfeger and published by . This book was released on 1989 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Turnpike Phenomenon and Infinite Horizon Optimal Control written by Alexander J. Zaslavski and published by Springer. This book was released on 2014-09-04 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the study of the turnpike phenomenon and describes the existence of solutions for a large variety of infinite horizon optimal control classes of problems. Chapter 1 provides introductory material on turnpike properties. Chapter 2 studies the turnpike phenomenon for discrete-time optimal control problems. The turnpike properties of autonomous problems with extended-value integrands are studied in Chapter 3. Chapter 4 focuses on large classes of infinite horizon optimal control problems without convexity (concavity) assumptions. In Chapter 5, the turnpike results for a class of dynamic discrete-time two-player zero-sum game are proven. This thorough exposition will be very useful for mathematicians working in the fields of optimal control, the calculus of variations, applied functional analysis and infinite horizon optimization. It may also be used as a primary text in a graduate course in optimal control or as supplementary text for a variety of courses in other disciplines. Researchers in other fields such as economics and game theory, where turnpike properties are well known, will also find this Work valuable.

Download or read book Turnpike theory discounted utility and the Von Neumann facet written by Lionel W. McKenzie and published by . This book was released on 1981 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Turnpike Theory Discounted Utility and the Von Neunanm Facet written by Lionel W. McKenzie and published by . This book was released on 1981 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Some Recent Developments in Economic Theory written by Frank Ward Kafer and published by . This book was released on 1965 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Maximal Economic Growth written by Jaroslav Vanek and published by . This book was released on 1968 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematical Theories of Economic Growth written by Edwin Burmeister and published by [New York] : Macmillan. This book was released on 1970 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Equilibrium Turnpike Theory with Constant Returns to Scale and Possible Heterogeneous Discount Factors written by Jeffrey L. Coles and published by . This book was released on 1983 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Turnpike Phenomenon and Symmetric Optimization Problems written by Alexander J. Zaslavski and published by Springer Nature. This book was released on 2022-04-11 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a leading expert in turnpike phenomenon, this book is devoted to the study of symmetric optimization, variational and optimal control problems in infinite dimensional spaces and turnpike properties of their approximate solutions. The book presents a systematic and comprehensive study of general classes of problems in optimization, calculus of variations, and optimal control with symmetric structures from the viewpoint of the turnpike phenomenon. The author establishes generic existence and well-posedness results for optimization problems and individual (not generic) turnpike results for variational and optimal control problems. Rich in impressive theoretical results, the author presents applications to crystallography and discrete dispersive dynamical systems which have prototypes in economic growth theory. This book will be useful for researchers interested in optimal control, calculus of variations turnpike theory and their applications, such as mathematicians, mathematical economists, and researchers in crystallography, to name just a few.

Download or read book Optimal Control Problems Related to the Robinson Solow Srinivasan Model written by Alexander J. Zaslavski and published by Springer Nature. This book was released on 2021-08-07 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the study of classes of optimal control problems arising in economic growth theory, related to the Robinson–Solow–Srinivasan (RSS) model. The model was introduced in the 1960s by economists Joan Robinson, Robert Solow, and Thirukodikaval Nilakanta Srinivasan and was further studied by Robinson, Nobuo Okishio, and Joseph Stiglitz. Since then, the study of the RSS model has become an important element of economic dynamics. In this book, two large general classes of optimal control problems, both of them containing the RSS model as a particular case, are presented for study. For these two classes, a turnpike theory is developed and the existence of solutions to the corresponding infinite horizon optimal control problems is established. The book contains 9 chapters. Chapter 1 discusses turnpike properties for some optimal control problems that are known in the literature, including problems corresponding to the RSS model. The first class of optimal control problems is studied in Chaps. 2–6. In Chap. 2, infinite horizon optimal control problems with nonautonomous optimality criteria are considered. The utility functions, which determine the optimality criterion, are nonconcave. This class of models contains the RSS model as a particular case. The stability of the turnpike phenomenon of the one-dimensional nonautonomous concave RSS model is analyzed in Chap. 3. The following chapter takes up the study of a class of autonomous nonconcave optimal control problems, a subclass of problems considered in Chap. 2. The equivalence of the turnpike property and the asymptotic turnpike property, as well as the stability of the turnpike phenomenon, is established. Turnpike conditions and the stability of the turnpike phenomenon for nonautonomous problems are examined in Chap. 5, with Chap. 6 devoted to the study of the turnpike properties for the one-dimensional nonautonomous nonconcave RSS model. The utility functions, which determine the optimality criterion, are nonconcave. The class of RSS models is identified with a complete metric space of utility functions. Using the Baire category approach, the turnpike phenomenon is shown to hold for most of the models. Chapter 7 begins the study of the second large class of autonomous optimal control problems, and turnpike conditions are established. The stability of the turnpike phenomenon for this class of problems is investigated further in Chaps. 8 and 9.