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Author: Alexander J. Zaslavski
Publisher: Springer Nature
ISBN: 3030969738
Category : Mathematics
Languages : en
Pages : 339
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Book Description
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.
Author: Alexander J. Zaslavski
Publisher: Springer Nature
ISBN: 3030969738
Category : Mathematics
Languages : en
Pages : 339
Get Book Here
Book Description
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.
Author: Alexander J. Zaslavski
Publisher:
ISBN: 9783030969745
Category :
Languages : en
Pages : 0
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Book Description
Author: Karl H. Pribram
Publisher: Routledge
ISBN: 1317729226
Category : Psychology
Languages : en
Pages : 728
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Book Description
The result of the second Appalachian conference on neurodynamics, this volume focuses on the problem of "order," its origins, evolution, and future. Central to this concern lies our understanding of time. Both classical and quantum physics have developed their conceptions within a framework of time symmetry. Divided into four major sections, this book: * provides refreshingly new approaches to the problem of the evolution of order, indicating the directions that need to be taken in subsequent conferences which will address learning and memory more directly; * addresses the issue of how information becomes transmitted in the nervous system; * shows how patterns are constructed at the synaptodendritic level of processing and how such pattern construction relates to image processing; and * deals with the control operations which operate on image processing to construct entities such as visual and auditory objects such as phonemes. The aim of the conference was to bring together professionals to exchange ideas -- some were fairly worked out; others were in their infancy. As a result, one of the most valuable aspects of the conference is that it fostered lasting interactive relationships among these leading researchers.
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: 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: 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: Leszek Gasinski
Publisher: CRC Press
ISBN: 9781584884842
Category : Mathematics
Languages : en
Pages : 992
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Book Description
Nonlinear analysis is a broad, interdisciplinary field characterized by a remarkable mixture of analysis, topology, and applications. Its concepts and techniques provide the tools for developing more realistic and accurate models for a variety of phenomena encountered in fields ranging from engineering and chemistry to economics and biology. This volume focuses on topics in nonlinear analysis pertinent to the theory of boundary value problems and their application in areas such as control theory and the calculus of variations. It complements the many other books on nonlinear analysis by addressing topics previously discussed fully only in scattered research papers. These include recent results on critical point theory, nonlinear differential operators, and related regularity and comparison principles. The rich variety of topics, both theoretical and applied, make Nonlinear Analysis useful to anyone, whether graduate student or researcher, working in analysis or its applications in optimal control, theoretical mechanics, or dynamical systems. An appendix contains all of the background material needed, and a detailed bibliography forms a guide for further study.
Author: Yves Achdou
Publisher: Springer Nature
ISBN: 3030598373
Category : Mathematics
Languages : en
Pages : 316
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Book Description
This volume provides an introduction to the theory of Mean Field Games, suggested by J.-M. Lasry and P.-L. Lions in 2006 as a mean-field model for Nash equilibria in the strategic interaction of a large number of agents. Besides giving an accessible presentation of the main features of mean-field game theory, the volume offers an overview of recent developments which explore several important directions: from partial differential equations to stochastic analysis, from the calculus of variations to modeling and aspects related to numerical methods. Arising from the CIME Summer School "Mean Field Games" held in Cetraro in 2019, this book collects together lecture notes prepared by Y. Achdou (with M. Laurière), P. Cardaliaguet, F. Delarue, A. Porretta and F. Santambrogio. These notes will be valuable for researchers and advanced graduate students who wish to approach this theory and explore its connections with several different fields in mathematics.
Author: Daron Acemoglu
Publisher: Princeton University Press
ISBN: 1400835771
Category : Business & Economics
Languages : en
Pages : 1009
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Book Description
From Nobel Prize–winning economist Daron Acemoglu, an incisive introduction to economic growth Introduction to Modern Economic Growth is a groundbreaking text from one of today's leading economists. Daron Acemoglu gives graduate students not only the tools to analyze growth and related macroeconomic problems, but also the broad perspective needed to apply those tools to the big-picture questions of growth and divergence. And he introduces the economic and mathematical foundations of modern growth theory and macroeconomics in a rigorous but easy to follow manner. After covering the necessary background on dynamic general equilibrium and dynamic optimization, the book presents the basic workhorse models of growth and takes students to the frontier areas of growth theory, including models of human capital, endogenous technological change, technology transfer, international trade, economic development, and political economy. The book integrates these theories with data and shows how theoretical approaches can lead to better perspectives on the fundamental causes of economic growth and the wealth of nations. Innovative and authoritative, this book is likely to shape how economic growth is taught and learned for years to come. Introduces all the foundations for understanding economic growth and dynamic macroeconomic analysis Focuses on the big-picture questions of economic growth Provides mathematical foundations Presents dynamic general equilibrium Covers models such as basic Solow, neoclassical growth, and overlapping generations, as well as models of endogenous technology and international linkages Addresses frontier research areas such as international linkages, international trade, political economy, and economic development and structural change An accompanying Student Solutions Manual containing the answers to selected exercises is available (978-0-691-14163-3/$24.95). See: https://press.princeton.edu/titles/8970.html For Professors only: To access a complete solutions manual online, email us at:
[email protected]
Author: M. K. Jha
Publisher: WIT Press
ISBN: 1845640039
Category : Transportation
Languages : en
Pages : 449
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Book Description
Addressing the intelligent concepts of the ancient endeavour of road design, this book discusses how a road alignment optimization model can be developed and applied in real case studies. Based on research in intelligent road design and alignment optimization, it is suitable for road planners, designers, senior undergraduate and graduate students.
