The use of a family of Gerstewitz scalarization functions in the context of vector optimization with variable domination structures to derive scalarization results

Abstract

In this paper, we study a nonlinear scalarization function for a variable domination structure in an arbitrary linear space without assuming any particular topology. Conditions are provided under which the nonlinear scalarization function possesses several useful properties such as finiteness, properness, positive homogeneity, subadditivity, (strict) monotonicity, convexity or continuity. These properties are employed to characterize approximate efficiency in linear spaces.

Keywords:

• Linear space
• variable domination structure
• nonlinear scalarization
• approximate efficiency

Mathematics Subject Classifications:

• 65K10
• 90C29
• 90C30

Acknowledgements

The authors would like to thank two anonymous referees so much for their valuable remarks and suggestions that helped significantly improve the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This is a result of the project supported by the Ministry of Education and Training of Viet Nam [grant number B2022-TCT-02].

Notes on contributors

Lam Quoc Anh

Lam Quoc Anh, is Professor, at the Department of Mathematics, Teacher College, Can Tho University, Can Tho City, Viet Nam. His research Interest are Applied mathematics, including existence and optimiality conditions, stability and senitivity analysis conditions, wellposedness conditions for optimization models, with publications of 80 papers.

Tran Ngoc Tam

Tran Ngoc Tam, Ph.D., is at Department of Mathematics, College of Natural Sciences, Can Tho University, Can Tho City, Viet Nam. His research Interest are Applied mathematics, including existence and optimiality conditions, stability and senitivity analysis conditions, wellposedness conditions for optimization models, with publications of 21 papers.