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A turnpike property for discrete–time control systems in metric spaces

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Optimization

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 32))

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Abstract

In this work we study the structure of “approximate” solutions for a nonautonomous infinite dimensional discrete-time control system determined by a sequence of continuous functions \(v_i: X \times X \to R^1\), \(i=0,\pm 1,\pm 2,\dots \) where X is a metric space.

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References

  1. Dzalilov, Z., Ivanov, A.F. and Rubinov, A.M. (2001) Difference inclusions with delay of economic growth,Dynam. Systems Appl., Vol. 10, pp. 283–293.

    MATH  MathSciNet  Google Scholar 

  2. Dzalilov, Z., Rubinov, A.M. and Kloeden, P.E. (1998) Lyapunov sequences and a turnpike theorem without convexity,Set-Valued Analysis, Vol. 6, pp. 277–302.

    Article  MATH  MathSciNet  Google Scholar 

  3. Leizarowitz, A. (1985) Infinite horizon autonomous systems with unbounded cost,Appl. Math. and Opt., Vol. 13, pp. 19–43.

    Article  MATH  MathSciNet  Google Scholar 

  4. Leizarowitz, A. (1989) Optimal trajectories on infinite horizon deterministic control systems,Appl. Math. and Opt., Vol. 19, pp. 11–32.

    Article  MATH  MathSciNet  Google Scholar 

  5. Leizarowitz, A. and Mizel, V.J. (1989) One dimensional infinite horizon variational problems arising in continuum mechanics,Arch. Rational Mech. Anal., Vol. 106, pp. 161–194.

    Article  MATH  MathSciNet  Google Scholar 

  6. Makarov, V.L, Levin, M.J. and Rubinov, A.M. (1995)Mathematical economic theory: pure and mixed types of economic mechanisms, North-Holland, Amsterdam.

    MATH  Google Scholar 

  7. Makarov, V.L. and Rubinov, A.M. (1973)Mathematical theory of economic dynamics and equilibria, Nauka, Moscow, English trans. (1977): Springer-Verlag, New York.

    Google Scholar 

  8. Mamedov, M.A. and Pehlivan, S. (2000) Statistical convergence of optimal paths,Math. Japon., Vol. 52, pp. 51–55.

    MATH  MathSciNet  Google Scholar 

  9. Mamedov, M.A. and Pehlivan, S. (2001) Statistical cluster points and turnpike theorem in nonconvex problems,J. Math. Anal. Appl., Vol. 256, pp. 686–693.

    Article  MATH  MathSciNet  Google Scholar 

  10. Marcus, M. and Zaslavski, A.J. (1999) The structure of extremals of a class of second order variational problems,Ann. Inst. H. Poincare, Anal. non lineare, Vol. 16, pp. 593–629.

    Article  MATH  MathSciNet  Google Scholar 

  11. McKenzie, L.W. (1976) Turnpike theory,Econometrica, Vol. 44, pp. 841–866.

    Article  MATH  MathSciNet  Google Scholar 

  12. Radner, R. (1961) Path of economic growth that are optimal with regard only to final states; a turnpike theorem,Rev. Econom. Stud., Vol. 28, pp. 98–104.

    Article  Google Scholar 

  13. Rubinov, A.M. (1980)Superlinear multivalued mappings and their applications to problems of mathematical economics, Nauka, Leningrad.

    Google Scholar 

  14. Rubinov, A.M. (1984) Economic dynamics,J. Soviet Math., Vol. 26, pp. 1975–2012.

    Article  MATH  Google Scholar 

  15. Samuelson, P.A. (1965) A catenary turnpike theorem involving consumption and the golden rule,American Economic Review, Vol. 55, pp. 486–496.

    Google Scholar 

  16. Zaslavski, A.J. (1995) Optimal programs on infinite horizon, 1 and 2,SIAM Journal on Control and Optimization, Vol. 33, pp. 1643–1686.

    Article  MATH  MathSciNet  Google Scholar 

  17. Zaslavski, A.J. (1996) Dynamic properties of optimal solutions of variational problems,Nonlinear Analysis: Theory, Methods and Applications, Vol. 27, pp. 895–932.

    Article  MATH  MathSciNet  Google Scholar 

  18. Zaslavski, A.J. (2000) Turnpike theorem for nonautonomous infinite dimensional discrete-time control systems,Optimization, Vol. 48, pp. 69–92.

    Article  MATH  MathSciNet  Google Scholar 

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Zaslavski, A.J. (2009). A turnpike property for discrete–time control systems in metric spaces. In: Pearce, C., Hunt, E. (eds) Optimization. Springer Optimization and Its Applications, vol 32. Springer, New York, NY. https://doi.org/10.1007/978-0-387-98096-6_7

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