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.
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Communicated by H.P. Benson.
This research was supported by the National Natural Science Foundation of China, Grant 10871141. The authors are grateful to Professor H.P. Benson, Professor F. Giannessi and the referees for valuable comments and suggestions, which have greatly improved the exposition. They also thank Professor G.Y. Chen for providing [6].
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Qiu, J.H., Hao, Y. Scalarization of Henig Properly Efficient Points in Locally Convex Spaces. J Optim Theory Appl 147, 71–92 (2010). https://doi.org/10.1007/s10957-010-9708-z
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DOI: https://doi.org/10.1007/s10957-010-9708-z