On the Generic Uniqueness of Pareto-Efficient Solutions of Vector Optimization Problems

In this paper, the generic uniqueness of Pareto weakly efficient solutions, especially Pareto-efficient solutions, of vector optimization problems is studied by using the nonlinear and linear scalarization methods, and some further results on the generic uniqueness are proved. These results present...

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Bibliographic Details
Published in:Mathematical problems in engineering 2021-07, Vol.2021, p.1-8
Main Authors: Zhang, Dejin, Xiang, Shuwen, Yang, Yanlong, Deng, Xicai
Format: Article
Language:English
Subjects:
Engineering
Euclidean space
Linear programming
Optimization
Pareto optimum
Uniqueness
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Summary:In this paper, the generic uniqueness of Pareto weakly efficient solutions, especially Pareto-efficient solutions, of vector optimization problems is studied by using the nonlinear and linear scalarization methods, and some further results on the generic uniqueness are proved. These results present that, for most of the vector optimization problems in the sense of the Baire category, the Pareto weakly efficient solution, especially the Pareto-efficient solution, is unique. Furthermore, based on these results, the generic Tykhonov well-posedness of vector optimization problems is given.
ISSN:1024-123X
1563-5147
DOI:10.1155/2021/6637841