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.
Acknowledgements
The authors would like to thank two anonymous referees so much for their valuable remarks and suggestions that helped significantly improve the paper.
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No potential conflict of interest was reported by the author(s).
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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.