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Isolated and Proper Efficiencies in Semi-Infinite Vector Optimization Problems

Author

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  • Thai Doan Chuong

    (Saigon University)

  • Jen-Chih Yao

    (Kaohsiung Medical University
    King Abdulaziz University)

Abstract

This paper deals with a nonsmooth semi-infinite multiobjective/vector optimization problem (SIMOP, for short). We first establish necessary and sufficient conditions for (local) strongly isolated solutions and (local) positively properly efficient solutions of an SIMOP. Then, we propose a dual problem to the SIMOP under consideration and examine weak and strong duality relations between them.

Suggested Citation

  • Thai Doan Chuong & Jen-Chih Yao, 2014. "Isolated and Proper Efficiencies in Semi-Infinite Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 447-462, August.
    • Handle: RePEc:spr:joptap:v:162:y:2014:i:2:d:10.1007_s10957-013-0425-2
    DOI: 10.1007/s10957-013-0425-2
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    References listed on IDEAS

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    1. P. H. Sach & D. S. Kim & G. M. Lee, 2006. "Strong Duality for Proper Efficiency in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 130(1), pages 139-151, July.
    2. N. Huy & D. Kim, 2013. "Lipschitz behavior of solutions to nonconvex semi-infinite vector optimization problems," Journal of Global Optimization, Springer, vol. 56(2), pages 431-448, June.
    3. T. Chuong & N. Huy & J. Yao, 2009. "Stability of semi-infinite vector optimization problems under functional perturbations," Computational Optimization and Applications, Springer, vol. 45(4), pages 583-595, December.
    4. Chuong, T.D. & Huy, N.Q. & Yao, J.C., 2010. "Pseudo-Lipschitz property of linear semi-infinite vector optimization problems," European Journal of Operational Research, Elsevier, vol. 200(3), pages 639-644, February.
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    Cited by:

    1. Le Thanh Tung, 2022. "Karush–Kuhn–Tucker optimality conditions and duality for multiobjective semi-infinite programming with vanishing constraints," Annals of Operations Research, Springer, vol. 311(2), pages 1307-1334, April.

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