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One-Dimensional Infinite Horizon Nonconcave Optimal Control Problems Arising in Economic Dynamics

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Abstract

We study the existence of optimal solutions for a class of infinite horizon nonconvex autonomous discrete-time optimal control problems. This class contains optimal control problems without discounting arising in economic dynamics which describe a model with a nonconcave utility function.

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References

  1. Anderson, B.D.O., Moore, J.B.: Linear Optimal Control. Prentice-Hall, Englewood Cliffs (1971)

    MATH  Google Scholar 

  2. Aubry, S., Le Daeron, P.Y.: The discrete Frenkel-Kontorova model and its extensions I. Physica D 8, 381–422 (1983)

    Article  MathSciNet  Google Scholar 

  3. Blot, J.: Infinite-horizon Pontryagin principles without invertibility. J. Nonlinear Convex Anal. 10, 177–189 (2009)

    MathSciNet  Google Scholar 

  4. Blot, J., Cartigny, P.: Optimality in infinite-horizon variational problems under sign conditions. J. Optim. Theory Appl. 106, 411–419 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  5. Coleman, B.D., Marcus, M., Mizel, V.J.: On the thermodynamics of periodic phases. Arch. Ration. Mech. Anal. 117, 321–347 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  6. Gale, D.: On optimal development in a multi-sector economy. Rev. Econ. Stud. 34, 1–18 (1967)

    Article  MathSciNet  Google Scholar 

  7. Jasso-Fuentes, H., Hernandez-Lerma, O.: Characterizations of overtaking optimality for controlled diffusion processes. Appl. Math. Optim. 57, 349–369 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. Leizarowitz, A.: Infinite horizon autonomous systems with unbounded cost. Appl. Math. Optim. 13, 19–43 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  9. Leizarowitz, A.: Tracking nonperiodic trajectories with the overtaking criterion. Appl. Math. Optim. 14, 155–171 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  10. Leizarowitz, A., Mizel, V.J.: One dimensional infinite horizon variational problems arising in continuum mechanics. Arch. Ration. Mech. Anal. 106, 161–194 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  11. Makarov, V.L., Rubinov, A.M.: Mathematical Theory of Economic Dynamics and Equilibria. Springer, Berlin (1977)

    MATH  Google Scholar 

  12. Marcus, M., Zaslavski, A.J.: The structure of extremals of a class of second order variational problems. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 16, 593–629 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  13. Mordukhovich, B.: Minimax design for a class of distributed parameter systems. Autom. Remote Control 50, 1333–1340 (1990)

    MathSciNet  Google Scholar 

  14. Mordukhovich, B., Shvartsman, I.: Optimization and feedback control of constrained parabolic systems under uncertain perturbations. In: Optimal Control, Stabilization and Nonsmooth Analysis. Lecture Notes Control Inform. Sci., pp. 121–132. Springer, Berlin (2004)

    Google Scholar 

  15. Pickenhain, S., Lykina, V.: Sufficiency conditions for infinite horizon optimal control problems. In: Recent Advances in Optimization. Proceedings of the 12th French-German-Spanish Conference on Optimization, Avignon, pp. 217–232. Springer, Berlin (2006)

    Google Scholar 

  16. Pickenhain, S., Lykina, V., Wagner, M.: On the lower semicontinuity of functionals involving Lebesgue or improper Riemann integrals in infinite horizon optimal control problems. Control Cybern. 37, 451–468 (2008)

    MathSciNet  Google Scholar 

  17. Prieto-Rumeau, T., Hernandez-Lerma, O.: Bias and overtaking equilibria for zero-sum continuous-time Markov games. Math. Methods Oper. Res. 61, 437–454 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  18. Rapaport, A., Cartigny, P.: Turnpike theorems by a value function approach. ESAIM Control Optim. Calc. Var. 10, 123–141 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  19. Rapaport, A., Cartigny, P.: Nonturnpike optimal solutions and their approximations in infinite horizon. J. Optim. Theory Appl. 134(1), 1–14 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  20. Zaslavski, A.J.: Ground states in Frenkel-Kontorova model. Math. USSR Izv. 29, 323–354 (1987)

    Article  Google Scholar 

  21. Zaslavski, A.J.: Turnpike Properties in the Calculus of Variations and Optimal Control. Springer, New York (2006)

    MATH  Google Scholar 

  22. Zaslavski, A.J.: Turnpike results for a discrete-time optimal control system arising in economic dynamics. Nonlinear Anal. 67, 2024–2049 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  23. Zaslavski, A.J.: Two turnpike results for a discrete-time optimal control systems. Nonlinear Anal. 71, 902–909 (2009)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Technion-Israel Institute of Technology, Haifa, 32000, Israel

    Alexander J. Zaslavski

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  1. Alexander J. Zaslavski
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Correspondence to Alexander J. Zaslavski.

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Communicating Editor: Frederic Bonnans.

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Zaslavski, A.J. One-Dimensional Infinite Horizon Nonconcave Optimal Control Problems Arising in Economic Dynamics. Appl Math Optim 64, 417–440 (2011). https://doi.org/10.1007/s00245-011-9146-9

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  • DOI: https://doi.org/10.1007/s00245-011-9146-9

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