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Efficiency and Generalized Concavity

Author

Listed:
  • D. T. Luc

    (Institute of Mathematics)

  • S. Schaible

    (University of California)

Abstract

In a recent paper on multiobjective maximization problems (Ref. 1), the authors use explicit quasiconcavity of the objective functions to prove a characterization of weakly efficient solutions and local-global properties. We provide results which are stronger in part and are derived with shorter proofs. We also present additional results.

Suggested Citation

  • D. T. Luc & S. Schaible, 1997. "Efficiency and Generalized Concavity," Journal of Optimization Theory and Applications, Springer, vol. 94(1), pages 147-153, July.
    • Handle: RePEc:spr:joptap:v:94:y:1997:i:1:d:10.1023_a:1022663804177
    DOI: 10.1023/A:1022663804177
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    References listed on IDEAS

    as
    1. A. Daniilidis & N. Hadjisavvas & S. Schaible, 1997. "Connectedness of the Efficient Set for Three-Objective Quasiconcave Maximization Problems," Journal of Optimization Theory and Applications, Springer, vol. 93(3), pages 517-524, June.
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    Citations

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    Cited by:

    1. Ovidiu Bagdasar & Nicolae Popovici, 2018. "Unifying local–global type properties in vector optimization," Journal of Global Optimization, Springer, vol. 72(2), pages 155-179, October.
    2. A. Guerraggio & D.T. Luc, 2003. "Optimality Conditions for C 1,1 Constrained Multiobjective Problems," Journal of Optimization Theory and Applications, Springer, vol. 116(1), pages 117-129, January.
    3. Z. M. Li & M. H. Zhan, 2007. "Optimality Conditions and Lagrange Duality for Vector Extremum Problems with Set Constraint," Journal of Optimization Theory and Applications, Springer, vol. 135(3), pages 323-332, December.
    4. Altannar Chinchuluun & Panos Pardalos, 2007. "A survey of recent developments in multiobjective optimization," Annals of Operations Research, Springer, vol. 154(1), pages 29-50, October.
    5. A. Guerraggio & D. T. Luc, 2001. "Optimality Conditions for C1,1 Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 615-629, June.

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