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Structure of Solutions of Variational Problems [electronic resource] /by Alexander J. Zaslavski.

by Zaslavski, Alexander J [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: SpringerBriefs in Optimization: Publisher: New York, NY : Springer New York : 2013.Description: VIII, 115 p. online resource.ISBN: 9781461463870.Subject(s): Mathematics | Computer software | Global analysis (Mathematics) | Functional equations | Mathematical optimization | Mathematics | Calculus of Variations and Optimal Control; Optimization | Difference and Functional Equations | Algorithm Analysis and Problem Complexity | AnalysisDDC classification: 515.64 Online resources: Click here to access online
Contents:
Preface -- 1. Introduction -- 2. Nonautonomous problems -- 3.Autonomous problems -- 4.Convex Autonomous Problems -- References -- Index.
In: Springer eBooksSummary: Structure of Solutions of Variational Problems is devoted to recent progress made in the studies of the structure of approximate solutions of variational problems considered on subintervals of a real line.  Results on properties of approximate solutions which are independent of the length of the interval, for all sufficiently large intervals are presented in a clear manner. Solutions, new approaches, techniques and methods to a number of difficult problems in the calculus of variations  are illustrated throughout this book. This book also contains significant results and information about the turnpike property of the variational problems. This well-known property is a general phenomenon which holds for large classes of variational problems. The author examines the following in relation to the turnpike property  in individual  (non-generic) turnpike results, sufficient and necessary conditions for the turnpike phenomenon as well as in the non-intersection property for extremals of variational problems. This book appeals to mathematicians  working in optimal control and the calculus as  well as with graduate students.
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Preface -- 1. Introduction -- 2. Nonautonomous problems -- 3.Autonomous problems -- 4.Convex Autonomous Problems -- References -- Index.

Structure of Solutions of Variational Problems is devoted to recent progress made in the studies of the structure of approximate solutions of variational problems considered on subintervals of a real line.  Results on properties of approximate solutions which are independent of the length of the interval, for all sufficiently large intervals are presented in a clear manner. Solutions, new approaches, techniques and methods to a number of difficult problems in the calculus of variations  are illustrated throughout this book. This book also contains significant results and information about the turnpike property of the variational problems. This well-known property is a general phenomenon which holds for large classes of variational problems. The author examines the following in relation to the turnpike property  in individual  (non-generic) turnpike results, sufficient and necessary conditions for the turnpike phenomenon as well as in the non-intersection property for extremals of variational problems. This book appeals to mathematicians  working in optimal control and the calculus as  well as with graduate students.

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