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Structure of Solutions of Variational Problems

  • Book
  • © 2013

Overview

Authors:
  1. Alexander J. Zaslavski

    1. , Department of Mathematics, Technion- Israel Institute of Technology, Haifa, Israel

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  • Looks into the current progress made in the study of the structure of approximate solutions of variational problems
  • Establishes a non-intersection property for optimal solutions over infinite horizon
  • Launches the strong turnpike property for autonomous variational problems

Part of the book series: SpringerBriefs in Optimization (BRIEFSOPTI)

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-viii
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  2. Introduction

    • Alexander J. Zaslavski
    Pages 1-5

  3. Nonautonomous Problems

    • Alexander J. Zaslavski
    Pages 7-45

  4. Autonomous Problems

    • Alexander J. Zaslavski
    Pages 47-82

  5. Convex Autonomous Problems

    • Alexander J. Zaslavski
    Pages 83-110

  6. Back Matter

    Pages 111-115
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Keywords

About this book

​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.​​​

Reviews

From the reviews:

“The book contains the most recent collection of various concepts, significant results and techniques about the turnpike property, which is a phenomenon that occurs for large classes of variational problems. … The book is supplemented by an almost exhaustive bibliography. It would probably be useful to give more applications of the results to specific problems to make the subject and the questions more appealing to non-expert researchers in the field and graduate students.” (Elvira Mascolo, zbMATH, Vol. 1272, 2013)

Authors and Affiliations

  • , Department of Mathematics, Technion- Israel Institute of Technology, Haifa, Israel

    Alexander J. Zaslavski

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