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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Turnpike property for extremals
of variational problems
with vector-valued functions


Author: A. J. Zaslavski
Journal: Trans. Amer. Math. Soc. 351 (1999), 211-231
MSC (1991): Primary 49J99, 58F99
DOI: https://doi.org/10.1090/S0002-9947-99-02132-7
MathSciNet review: 1458340
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Abstract: In this paper we study the structure of extremals $\nu\colon[0,T]\to R^n$ of variational problems with large enough $T$, fixed end points and an integrand $f$ from a complete metric space of functions. We will establish the turnpike property for a generic integrand $f$. Namely, we will show that for a generic integrand $f$, any small $\varepsilon>0$ and an extremal $\nu\colon[0,T]\to R^n$ of the variational problem with large enough $T$, fixed end points and the integrand $f$, for each $\tau\in[L_1, T-L_1]$ the set $\{\nu(t)\colon t\in[\tau,\tau+L_2]\}$ is equal to a set $H(f)$ up to $\varepsilon$ in the Hausdorff metric. Here $H(f)\subset R^n$ is a compact set depending only on the integrand $f$ and $L_1>L_2>0$ are constants which depend only on $\varepsilon$ and $|\nu(0)|$, $|\nu(T)|$.


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Additional Information

A. J. Zaslavski
Affiliation: Department of Mathematics, Technion-Israel Institute of Technology, Haifa, 32000, Israel
Email: ajzasl@techunix.technion.ac.il

DOI: https://doi.org/10.1090/S0002-9947-99-02132-7
Keywords: Good function, turnpike property, representation formula, minimal long-run average cost growth rate
Received by editor(s): September 29, 1995
Received by editor(s) in revised form: November 18, 1996
Article copyright: © Copyright 1999 American Mathematical Society