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Scalarization of Henig Properly Efficient Points in Locally Convex Spaces

Author

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  • J. H. Qiu

    (Suzhou University)

  • Y. Hao

    (Suzhou University)

Abstract

Without any convexity assumption on feasible sets, we obtain two versions of scalarization of Henig properly efficient points with respect to a base of the ordering cone. Then we further deduce two corresponding versions of the scalarization of (resp. generalized) Henig properly efficient points, which only depend on the ordering cone, not referring to any special base. Moreover, we investigate the relationship between generalized Henig properly efficient points and Henig properly efficient points. Particularly, we give some conditions for generalized Henig properly efficient points to be Henig properly efficient points.

Suggested Citation

  • J. H. Qiu & Y. Hao, 2010. "Scalarization of Henig Properly Efficient Points in Locally Convex Spaces," Journal of Optimization Theory and Applications, Springer, vol. 147(1), pages 71-92, October.
    • Handle: RePEc:spr:joptap:v:147:y:2010:i:1:d:10.1007_s10957-010-9708-z
    DOI: 10.1007/s10957-010-9708-z
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    References listed on IDEAS

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    1. X. Y. Zheng, 1997. "Proper Efficiency in Locally Convex Topological Vector Spaces," Journal of Optimization Theory and Applications, Springer, vol. 94(2), pages 469-486, August.
    2. X. Y. Zheng, 2000. "Scalarization of Henig Proper Efficient Points in a Normed Space," Journal of Optimization Theory and Applications, Springer, vol. 105(1), pages 233-247, April.
    3. J. H. Qiu, 2007. "Superefficiency in Local Convex Spaces," Journal of Optimization Theory and Applications, Springer, vol. 135(1), pages 19-35, October.
    4. G. Y. Chen & C. J. Goh & X. Q. Yang, 1999. "Vector network equilibrium problems and nonlinear scalarization methods," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 49(2), pages 239-253, April.
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    Cited by:

    1. C. S. Lalitha & Prashanto Chatterjee, 2012. "Stability and Scalarization of Weak Efficient, Efficient and Henig Proper Efficient Sets Using Generalized Quasiconvexities," Journal of Optimization Theory and Applications, Springer, vol. 155(3), pages 941-961, December.
    2. C. S. Lalitha & Prashanto Chatterjee, 2015. "Stability and Scalarization in Vector Optimization Using Improvement Sets," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 825-843, September.

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