Author(s)

Yucheng Pan ¹, Dongyu Lan ¹

Affiliation(s)

¹ Faculty of Science, Beijing University of Technology, Beijing, 100124, China

Corresponding Author

Yucheng Pan

ABSTRACT

In this paper, we study the existence of minimal elements of lower-C semicontinuous vector-valued mappings on compact sets and properly quasi-convex vector-valued mappings on compact convex sets in the sense of lexicographic order, the first and second criteria for the existence of minimal elements are obtained. In addition, this paper illustrates the extensive application of the first criterion in the field of discontinuous vector-valued mapping and the stronger applicability of the second criterion compared with the first criterion.

KEYWORDS

Lexicographic order, minimal element, lower-C semicontinuous, properly quasi-convex

CITE THIS PAPER

Yucheng Pan, Dongyu Lan, The Condition of Reaching the Minimum of Vector-Valued Mapping under Lexicographic Order. Journal of Network Computing and Applications (2022) Vol. 7: 14-19. DOI: http://dx.doi.org/10.23977/jnca.2022.070104.

REFERENCES

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[3] X.B.Li, S.J.Li, Z.M. Fang. A minimax theorem for vector-valued functions in lexicographic order [J]. Nonlinear Analysis, 73(2010): 1101-1108.
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