Structure of Solutions of Variational Problems

  • Alexander J. Zaslavski

Part of the SpringerBriefs in Optimization book series (BRIEFSOPTI)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Alexander J. Zaslavski
    Pages 1-5
  3. Alexander J. Zaslavski
    Pages 7-45
  4. Alexander J. Zaslavski
    Pages 47-82
  5. Alexander J. Zaslavski
    Pages 83-110
  6. Back Matter
    Pages 111-115

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.​​​


agreeable solution approximate solution asymptotic turnpike property autonomous problems nonintersection property turnpike property

Authors and affiliations

  • Alexander J. Zaslavski
    • 1
  1. 1., Department of MathematicsTechnion- Israel Institute of TechnologyHaifaIsrael

Bibliographic information