Turnpike Phenomenon And Symmetric Optimization Problems
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Author | : Alexander J. Zaslavski |
Publisher | : |
Total Pages | : 0 |
Release | : 2022 |
Genre | : |
ISBN | : 9783030969745 |
Download Turnpike Phenomenon and Symmetric Optimization Problems Book in PDF, Epub and Kindle
Author | : Alexander J. Zaslavski |
Publisher | : Springer Nature |
Total Pages | : 339 |
Release | : 2022-04-11 |
Genre | : Mathematics |
ISBN | : 3030969738 |
Download Turnpike Phenomenon and Symmetric Optimization Problems Book in PDF, Epub and Kindle
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 |
Total Pages | : 377 |
Release | : 2014-09-04 |
Genre | : Mathematics |
ISBN | : 3319088289 |
Download Turnpike Phenomenon and Infinite Horizon Optimal Control Book in PDF, Epub and Kindle
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 Zaslavski |
Publisher | : Springer Science & Business Media |
Total Pages | : 442 |
Release | : 2005-08-25 |
Genre | : Mathematics |
ISBN | : 9780387281551 |
Download Turnpike Properties in the Calculus of Variations and Optimal Control Book in PDF, Epub and Kindle
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 |
Total Pages | : 570 |
Release | : 2020-08-14 |
Genre | : Mathematics |
ISBN | : 9783030201807 |
Download Turnpike Conditions in Infinite Dimensional Optimal Control Book in PDF, Epub and Kindle
This book provides a comprehensive study of turnpike phenomenon arising in optimal control theory. The focus is on individual (non-generic) turnpike results which are both mathematically significant and have numerous applications in engineering and economic theory. All results obtained in the book are new. New approaches, techniques, and methods are rigorously presented and utilize research from finite-dimensional variational problems and discrete-time optimal control problems to find the necessary conditions for the turnpike phenomenon in infinite dimensional spaces. The semigroup approach is employed in the discussion as well as PDE descriptions of continuous-time dynamics. The main results on sufficient and necessary conditions for the turnpike property are completely proved and the numerous illustrative examples support the material for the broad spectrum of experts. Mathematicians interested in the calculus of variations, optimal control and in applied functional analysis will find this book a useful guide to the turnpike phenomenon in infinite dimensional spaces. Experts in economic and engineering modeling as well as graduate students will also benefit from the developed techniques and obtained results.
Author | : Alexander J. Zaslavski |
Publisher | : Springer Nature |
Total Pages | : 448 |
Release | : 2021-01-04 |
Genre | : Mathematics |
ISBN | : 3030603075 |
Download Turnpike Theory for the Robinson–Solow–Srinivasan Model Book in PDF, Epub and Kindle
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.
Author | : Alexander J. Zaslavski |
Publisher | : |
Total Pages | : 0 |
Release | : 2023 |
Genre | : |
ISBN | : 9783031272097 |
Download Turnpike Phenomenon in Metric Spaces Book in PDF, Epub and Kindle
This book is devoted to the study of the turnpike phenomenon arising in optimal control theory. Special focus is placed on Turnpike results, in sufficient and necessary conditions for the turnpike phenomenon and in its stability under small perturbations of objective functions. The most important feature of this book is that it develops a large, general class of optimal control problems in metric space. Additional value is in the provision of solutions to a number of difficult and interesting problems in optimal control theory in metric spaces. Mathematicians working in optimal control, optimization, and experts in applications of optimal control to economics and engineering, will find this book particularly useful. All main results obtained in the book are new. The monograph contains nine chapters. Chapter 1 is an introduction. Chapter 2 discusses Banach space valued functions, set-valued mappings in infinite dimensional spaces, and related continuous-time dynamical systems. Some convergence results are obtained. In Chapter 3, a discrete-time dynamical system with a Lyapunov function in a metric space induced by a set-valued mapping, is studied. Chapter 4 is devoted to the study of a class of continuous-time dynamical systems, an analog of the class of discrete-time dynamical systems considered in Chapter 3. Chapter 5 develops a turnpike theory for a class of general dynamical systems in a metric space with a Lyapunov function. Chapter 6 contains a study of the turnpike phenomenon for discrete-time nonautonomous problems on subintervals of half-axis in metric spaces, which are not necessarily compact. Chapter 7 contains preliminaries which are needed in order to study turnpike properties of infinite-dimensional optimal control problems. In Chapter 8, sufficient and necessary conditions for the turnpike phenomenon for continuous-time optimal control problems on subintervals of the half-axis in metric spaces, is established. In Chapter 9, the examination continues of the turnpike phenomenon for the continuous-time optimal control problems on subintervals of half-axis in metric spaces discussed in Chapter 8.
Author | : Gunther Schwerdtfeger |
Publisher | : |
Total Pages | : 60 |
Release | : 1989 |
Genre | : |
ISBN | : 9780387508801 |
Download Weiterbildungsnormen der Ärztekammern auf dem rechtlichen Prüfstand Book in PDF, Epub and Kindle
Author | : Karl H. Pribram |
Publisher | : Routledge |
Total Pages | : 728 |
Release | : 2018-10-24 |
Genre | : Psychology |
ISBN | : 1317729226 |
Download Origins Book in PDF, Epub and Kindle
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 Nature |
Total Pages | : 132 |
Release | : 2022-09-29 |
Genre | : Mathematics |
ISBN | : 3031126440 |
Download Optimization in Banach Spaces Book in PDF, Epub and Kindle
The book is devoted to the study of constrained minimization problems on closed and convex sets in Banach spaces with a Frechet differentiable objective function. Such problems are well studied in a finite-dimensional space and in an infinite-dimensional Hilbert space. When the space is Hilbert there are many algorithms for solving optimization problems including the gradient projection algorithm which is one of the most important tools in the optimization theory, nonlinear analysis and their applications. An optimization problem is described by an objective function and a set of feasible points. For the gradient projection algorithm each iteration consists of two steps. The first step is a calculation of a gradient of the objective function while in the second one we calculate a projection on the feasible set. In each of these two steps there is a computational error. In our recent research we show that the gradient projection algorithm generates a good approximate solution, if all the computational errors are bounded from above by a small positive constant. It should be mentioned that the properties of a Hilbert space play an important role. When we consider an optimization problem in a general Banach space the situation becomes more difficult and less understood. On the other hand such problems arise in the approximation theory. The book is of interest for mathematicians working in optimization. It also can be useful in preparation courses for graduate students. The main feature of the book which appeals specifically to this audience is the study of algorithms for convex and nonconvex minimization problems in a general Banach space. The book is of interest for experts in applications of optimization to the approximation theory. In this book the goal is to obtain a good approximate solution of the constrained optimization problem in a general Banach space under the presence of computational errors. It is shown that the algorithm generates a good approximate solution, if the sequence of computational errors is bounded from above by a small constant. The book consists of four chapters. In the first we discuss several algorithms which are studied in the book and prove a convergence result for an unconstrained problem which is a prototype of our results for the constrained problem. In Chapter 2 we analyze convex optimization problems. Nonconvex optimization problems are studied in Chapter 3. In Chapter 4 we study continuous algorithms for minimization problems under the presence of computational errors. The algorithm generates a good approximate solution, if the sequence of computational errors is bounded from above by a small constant. The book consists of four chapters. In the first we discuss several algorithms which are studied in the book and prove a convergence result for an unconstrained problem which is a prototype of our results for the constrained problem. In Chapter 2 we analyze convex optimization problems. Nonconvex optimization problems are studied in Chapter 3. In Chapter 4 we study continuous algorithms for minimization problems under the presence of computational errors.