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Enhanced Efficiency in Multi-objective Optimization

Author

Listed:
  • Y. Jiang

    (Nanjing University of Information Science and Technology)

  • S. Deng

    (Northern Illinois University)

Abstract

For a given multi-objective optimization problem, we introduce and study the notion of α-proper efficiency. We give two characterizations of such proper efficiency: one is in terms of exact penalization and the other is in terms of stability of associated parametric problems. Applying the aforementioned characterizations and recent results on global error bounds for inequality systems, we obtain verifiable conditions for α-proper efficiency. For a large class of polynomial multi-objective optimization problems, we show that any efficient solution is α-properly efficient under some mild conditions. For a convex quadratically constrained multi-objective optimization problem with convex quadratic objective functions, we show that any efficient solution is α-properly efficient with a known estimate on α whenever its constraint set is bounded. Finally, we illustrate our achieved results with examples, and give an example to show that such an enhanced efficiency property may not hold for multi-objective optimization problems involving C ∞-functions as objective functions.

Suggested Citation

  • Y. Jiang & S. Deng, 2014. "Enhanced Efficiency in Multi-objective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 577-588, August.
    • Handle: RePEc:spr:joptap:v:162:y:2014:i:2:d:10.1007_s10957-013-0486-2
    DOI: 10.1007/s10957-013-0486-2
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    References listed on IDEAS

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    1. S. Deng, 1998. "On Efficient Solutions in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 96(1), pages 201-209, January.
    2. Alexander J. Zaslavski, 2010. "Optimization on Metric and Normed Spaces," Springer Optimization and Its Applications, Springer, number 978-0-387-88621-3, June.
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