The Turnpike Property for Approximate Solutions of Variational Problems

  • Alexander J. Zaslavski
Part of the Springer Optimization and Its Applications book series (SOIA, volume 82)


In this chapter we study the structure of approximate solutions of variational problems with continuous integrands \(f : [0,\infty ) \times {R}^{n} \times {R}^{n} \rightarrow {R}^{1}\) which belong to a complete metric space of functions \(\mathfrak{M}\). We do not impose any convexity assumption and establish the existence of an everywhere dense G δ -set \(\mathcal{F}\subset \mathfrak{M}\) such that each integrand in \(\mathcal{F}\) has the turnpike property.


  1. 96.
    Zaslavski AJ (2004) The turnpike property for approximate solutions of variational problems without convexity. Nonlinear Anal 58:547–569MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

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

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