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Author: Alexander J. Zaslavski
Publisher: Springer Science & Business Media
ISBN: 0387281541
Category : Mathematics
Languages : en
Pages : 407
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Book Description
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.
Author: Alexander J. Zaslavski
Publisher: Springer Science & Business Media
ISBN: 0387281541
Category : Mathematics
Languages : en
Pages : 407
Get Book Here
Book Description
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.
Author: Dean A. Carlson
Publisher: Springer Science & Business Media
ISBN: 3662025299
Category : Business & Economics
Languages : en
Pages : 270
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Book Description
This monograph deals with various classes of deterministic continuous time optimal control problems wh ich are defined over unbounded time intervala. For these problems, the performance criterion is described by an improper integral and it is possible that, when evaluated at a given admissible element, this criterion is unbounded. To cope with this divergence new optimality concepts; referred to here as "overtaking", "weakly overtaking", "agreeable plans", etc. ; have been proposed. The motivation for studying these problems arisee primarily from the economic and biological aciences where models of this nature arise quite naturally since no natural bound can be placed on the time horizon when one considers the evolution of the state of a given economy or species. The reeponsibility for the introduction of this interesting class of problems rests with the economiste who first studied them in the modeling of capital accumulation processes. Perhaps the earliest of these was F. Ramsey who, in his seminal work on a theory of saving in 1928, considered a dynamic optimization model defined on an infinite time horizon. Briefly, this problem can be described as a "Lagrange problem with unbounded time interval". The advent of modern control theory, particularly the formulation of the famoue Maximum Principle of Pontryagin, has had a considerable impact on the treatment of these models as well as optimization theory in general.
Author: Alexander J. Zaslavski
Publisher: Springer Nature
ISBN: 981169298X
Category : Mathematics
Languages : en
Pages : 387
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Book Description
This book is devoted to the study of two large classes of discrete-time optimal control problems arising in mathematical economics. Nonautonomous optimal control problems of the first class are determined by a sequence of objective functions and sequence of constraint maps. They correspond to a general model of economic growth. We are interested in turnpike properties of approximate solutions and in the stability of the turnpike phenomenon under small perturbations of objective functions and constraint maps. The second class of autonomous optimal control problems corresponds to another general class of models of economic dynamics which includes the Robinson–Solow–Srinivasan model as a particular case. In Chap. 1 we discuss turnpike properties for a large class of discrete-time optimal control problems studied in the literature and for the Robinson–Solow–Srinivasan model. In Chap. 2 we introduce the first class of optimal control problems and study its turnpike property. This class of problems is also discussed in Chaps. 3–6. In Chap. 3 we study the stability of the turnpike phenomenon under small perturbations of the objective functions. Analogous results for problems with discounting are considered in Chap. 4. In Chap. 5 we study the stability of the turnpike phenomenon under small perturbations of the objective functions and the constraint maps. Analogous results for problems with discounting are established in Chap. 6. The results of Chaps. 5 and 6 are new. The second class of problems is studied in Chaps. 7–9. In Chap. 7 we study the turnpike properties. The stability of the turnpike phenomenon under small perturbations of the objective functions is established in Chap. 8. In Chap. 9 we establish the stability of the turnpike phenomenon under small perturbations of the objective functions and the constraint maps. The results of Chaps. 8 and 9 are new. In Chap. 10 we study optimal control problems related to a model of knowledge-based endogenous economic growth and show the existence of trajectories of unbounded economic growth and provide estimates for the growth rate.
Author: Thomas A. Weber
Publisher: MIT Press
ISBN: 0262015730
Category : Business & Economics
Languages : en
Pages : 387
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Book Description
A rigorous introduction to optimal control theory, with an emphasis on applications in economics. This book bridges optimal control theory and economics, discussing ordinary differential equations, optimal control, game theory, and mechanism design in one volume. Technically rigorous and largely self-contained, it provides an introduction to the use of optimal control theory for deterministic continuous-time systems in economics. The theory of ordinary differential equations (ODEs) is the backbone of the theory developed in the book, and chapter 2 offers a detailed review of basic concepts in the theory of ODEs, including the solution of systems of linear ODEs, state-space analysis, potential functions, and stability analysis. Following this, the book covers the main results of optimal control theory, in particular necessary and sufficient optimality conditions; game theory, with an emphasis on differential games; and the application of control-theoretic concepts to the design of economic mechanisms. Appendixes provide a mathematical review and full solutions to all end-of-chapter problems. The material is presented at three levels: single-person decision making; games, in which a group of decision makers interact strategically; and mechanism design, which is concerned with a designer's creation of an environment in which players interact to maximize the designer's objective. The book focuses on applications; the problems are an integral part of the text. It is intended for use as a textbook or reference for graduate students, teachers, and researchers interested in applications of control theory beyond its classical use in economic growth. The book will also appeal to readers interested in a modeling approach to certain practical problems involving dynamic continuous-time models.
Author: Gustav Feichtinger
Publisher: Springer
ISBN: 3319751697
Category : Business & Economics
Languages : en
Pages : 443
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Book Description
Since the days of Lev Pontryagin and his associates, the discipline of Optimal Control has enjoyed a tremendous upswing – not only in terms of its mathematical foundations, but also with regard to numerous fields of application, which have given rise to highly active research areas. Few scholars, however, have been able to make contributions to both the mathematical developments and the (socio-)economic applications; Vladimir Veliov is one of them. In the course of his scientific career, he has contributed highly influential research on mathematical aspects of Optimal Control Theory, as well as applications in Economics and Operations Research. One of the hallmarks of his research is its impressive breadth. This volume, published on the occasion of his 65th birthday, accurately reflects that diversity. The mathematical aspects covered include stability theory for difference inclusions, metric regularity, generalized duality theory, the Bolza problem from a functional analytic perspective, and fractional calculus. In turn, the book explores various applications of control theory, such as population dynamics, population economics, epidemiology, optimal growth theory, resource and energy economics, environmental management, and climate change. Further topics include optimal liquidity, dynamics of the firm, and wealth inequality.
Author: Alexander J. Zaslavski
Publisher: Springer
ISBN: 3319088289
Category : Mathematics
Languages : en
Pages : 377
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Book Description
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.
Author:
Publisher: Elsevier
ISBN: 0323853390
Category : Mathematics
Languages : en
Pages : 596
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Book Description
Numerical Control: Part A, Volume 23 in the Handbook of Numerical Analysis series, highlights new advances in the field, with this new volume presenting interesting chapters written by an international board of authors. Chapters in this volume include Numerics for finite-dimensional control systems, Moments and convex optimization for analysis and control of nonlinear PDEs, The turnpike property in optimal control, Structure-Preserving Numerical Schemes for Hamiltonian Dynamics, Optimal Control of PDEs and FE-Approximation, Filtration techniques for the uniform controllability of semi-discrete hyperbolic equations, Numerical controllability properties of fractional partial differential equations, Optimal Control, Numerics, and Applications of Fractional PDEs, and much more. - Provides the authority and expertise of leading contributors from an international board of authors - Presents the latest release in the Handbook of Numerical Analysis series - Updated release includes the latest information on Numerical Control
Author: Dominique Bonvin
Publisher: MDPI
ISBN: 303842448X
Category : Electronic book
Languages : en
Pages : 255
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Book Description
This book is a printed edition of the Special Issue "Real-Time Optimization" that was published in Processes
Author: John D. Hedengren
Publisher: MDPI
ISBN: 3038428051
Category : Technology & Engineering
Languages : en
Pages : 175
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Book Description
This book is a printed edition of the Special Issue "Combined Scheduling and Control" that was published in Processes
Author: N.V. Hritonenko
Publisher: Springer Science & Business Media
ISBN: 1461334462
Category : Mathematics
Languages : en
Pages : 282
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Book Description
Modern economic growth is characterized by structural changes based on the introduction of new technologies into economics. The replacement and renova tion of technologies in industrial environments undergoing technical change is clearly one of the key aspects of economic development. The mathematical modeling of evolutionary economics under technical change (TC) has been rigorously considered by many authors during last decades. There is a wide variety of economic approaches and models describing different aspects of technical change. Among these are the models of embodied technical progress [19], [35], [70], [129], endogenous growth models [94], [102], the models of technological innovations [31], [32], [41], and others. The perspective self organization evolutionary approach is developed in [20], [38], [122], [123], [124], [126], which unites the aspects of diffusion of new technologies, technological and behavioral diversity of firms, learning mechanisms, age-dependent effects, and other important features of real-life economics. On the whole, an interest in evolutionary economics has brought considerable progress in the description and conceptualization of the sources, characteristics, direction and effects of technical change [125]. However, the modeling and control of technology lifetime under technical change has received rather little attention in mathematical economics in con trary to other aspects of technical progress. The lifetime of technologies has rarely been formally treated as a part of more general mathematical theory of economic dynamics. A problem which is still to be resolved consists in establishing the rational strategies of technologies' replacement under various assumptions on the behavior of technical change.
