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Stability Results for Efficient Solutions of Vector Optimization Problems

Author

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  • S. W. Xiang

    (Guizhou University)

  • W. S. Yin

    (Guizhou University)

Abstract

Using the additive weight method of vector optimization problems and the method of essential solutions, we study some continuity properties of the mapping which associates the set of efficient solutions S(f) to the objective function f. To understand such properties, the key point is to consider the stability of additive weight solutions and the relationship between efficient solutions and additive weight solutions.

Suggested Citation

  • S. W. Xiang & W. S. Yin, 2007. "Stability Results for Efficient Solutions of Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 134(3), pages 385-398, September.
    • Handle: RePEc:spr:joptap:v:134:y:2007:i:3:d:10.1007_s10957-007-9214-0
    DOI: 10.1007/s10957-007-9214-0
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    References listed on IDEAS

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    1. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    2. E. Miglierina & E. Molho, 2002. "Scalarization and Stability in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 114(3), pages 657-670, September.
    3. X. X. Huang, 2000. "Stability in vector-valued and set-valued optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(2), pages 185-193, November.
    4. E. Miglierina & E. Molho & M. Rocca, 2005. "Well-Posedness and Scalarization in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 126(2), pages 391-409, August.
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    Cited by:

    1. T. Chuong & A. Kruger & J.-C. Yao, 2011. "Calmness of efficient solution maps in parametric vector optimization," Journal of Global Optimization, Springer, vol. 51(4), pages 677-688, December.
    2. Y. D. Xu & S. J. Li, 2016. "On the solution continuity of parametric set optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(1), pages 223-237, August.
    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. Rubén López, 2013. "Variational convergence for vector-valued functions and its applications to convex multiobjective optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(1), pages 1-34, August.

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