Characterization of variable domination structures via nonlinear scalarization

Authors:
G. Y. Chen;X. Q. Yang
Affiliations:
Professor, Institute of Systems Science, Chinese Academy of Sciences, Beijing, PRC;Associate Professor, Department of Applied Mathematics, Hong Kong Polytechnic University, Kowloon, Hong Kong
Venue:
Journal of Optimization Theory and Applications
Year:
2002

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Abstract

In this paper, a nonlinear scalarization function is introduced for a variable domination structure. It is shown that this function is positively homogeneous, subadditive, and strictly monotone. This nonlinear function is then applied to characterize the weakly nondominated solution of multicriteria decision making problems and the solution of vector variational inequalities.