On the Generic Uniqueness of Pareto-Efficient Solutions of Vector Optimization Problems. (12th July 2021)

• Record Type: Journal Article
• Authors: Zhang, Dejin; Xiang, Shuwen; Yang, Yanlong; Deng, Xicai
• Other Names: Mesbah Mahmoud Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2021(2021)
• Publication Date: 2021-07-12
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2021/6637841
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : 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.