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Reciprocal Optimal Control Problems and the Associated Pareto Frontier

Author

Listed:
  • L. Grosset

    (University of Padova)

  • B. Viscolani

    (University of Padova)

Abstract

It is well known that, if a control is Pareto optimal for a multiobjective optimal control problem, then it satisfies the necessary conditions of an optimal control problem with isoperimetric constraints. We introduce a set of sufficient conditions reversing that implication. Thus, we study some properties of the isoperimetric problems and their applications to the analysis of economic models.

Suggested Citation

  • L. Grosset & B. Viscolani, 2006. "Reciprocal Optimal Control Problems and the Associated Pareto Frontier," Journal of Optimization Theory and Applications, Springer, vol. 130(1), pages 113-123, July.
    • Handle: RePEc:spr:joptap:v:130:y:2006:i:1:d:10.1007_s10957-006-9089-5
    DOI: 10.1007/s10957-006-9089-5
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    References listed on IDEAS

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    1. Caputo,Michael R., 2005. "Foundations of Dynamic Economic Analysis," Cambridge Books, Cambridge University Press, number 9780521842723, January.
    2. Takayama,Akira, 1985. "Mathematical Economics," Cambridge Books, Cambridge University Press, number 9780521314985.
    3. M. R. Caputo, 1998. "Economic Characterization of Reciprocal Isoperimetric Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 325-350, August.
    4. M. R. Caputo, 1999. "Economic Characterization of Reciprocal Isoperimetric Control Problems Revisited," Journal of Optimization Theory and Applications, Springer, vol. 101(3), pages 723-730, June.
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    Cited by:

    1. Haijun Liu & Neng Fan & Panos M. Pardalos, 2012. "Generalized Lagrange Function and Generalized Weak Saddle Points for a Class of Multiobjective Fractional Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 154(2), pages 370-381, August.
    2. C. Kaya & Helmut Maurer, 2014. "A numerical method for nonconvex multi-objective optimal control problems," Computational Optimization and Applications, Springer, vol. 57(3), pages 685-702, April.

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