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Multicriterion Aerodynamic Shape Design Optimization and Inverse Problems Using Control Theory and Nash Games

Author

Listed:
  • Z. Tang

    (Nanjing University of Aeronautics and Astronautics)

  • J.-A. Désidéri

    (INRIA)

  • J. Périaux

    (UPC)

Abstract

Multicriterion design is gaining importance in aeronautics in order to cope with new needs of society. In the literature, contributions to single discipline and/or single-point design optimization abound. The goal of this paper is to introduce a new approach combining the adjoint method with a formulation derived from game theory for multipoint aerodynamic design problems. Transonic flows around lifting airfoils are analyzed via Euler computations. Airfoil shapes are optimized according to various aerodynamic criteria. The notion of player is introduced. In a competitive Nash game, each player attempts to optimize its own criterion through a symmetric exchange of information with others. A Nash equilibrium is reached when each player, constrained by the strategy of the others, cannot improve further its own criterion. Specific real and virtual symmetric Nash games are implemented to set up an optimization strategy for design under conflict.

Suggested Citation

  • Z. Tang & J.-A. Désidéri & J. Périaux, 2007. "Multicriterion Aerodynamic Shape Design Optimization and Inverse Problems Using Control Theory and Nash Games," Journal of Optimization Theory and Applications, Springer, vol. 135(3), pages 599-622, December.
    • Handle: RePEc:spr:joptap:v:135:y:2007:i:3:d:10.1007_s10957-007-9255-4
    DOI: 10.1007/s10957-007-9255-4
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    Cited by:

    1. François Gallard & Bijan Mohammadi & Marc Montagnac & Matthieu Meaux, 2015. "An Adaptive Multipoint Formulation for Robust Parametric Optimization," Journal of Optimization Theory and Applications, Springer, vol. 167(2), pages 693-715, November.
    2. Anna N. Rettieva, 2022. "Dynamic multicriteria games with asymmetric players," Journal of Global Optimization, Springer, vol. 83(3), pages 521-537, July.
    3. Axel Dreves & Joachim Gwinner, 2016. "Jointly Convex Generalized Nash Equilibria and Elliptic Multiobjective Optimal Control," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 1065-1086, March.

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