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Mathematics | Structure of Solutions of Variational Problems

Structure of Solutions of Variational Problems

Zaslavski, Alexander J.

2013, VIII, 115 p.

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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
​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.​​​

Content Level » Research

Keywords » agreeable solution - approximate solution - asymptotic turnpike property - autonomous problems - nonintersection property - turnpike property

Related subjects » Analysis - Dynamical Systems & Differential Equations - Mathematics - Theoretical Computer Science

Table of contents 

Preface.- 1. Introduction.- 2. Nonautonomous problems.- 3.Autonomous problems.- 4.Convex Autonomous Problems.- References.- Index.

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