The aim of this paper is to investigate the continuity of solution mappings for para-metric set optimization problems with upper and lower set less order relations by scalarization methods.First,we recall some linear ...The aim of this paper is to investigate the continuity of solution mappings for para-metric set optimization problems with upper and lower set less order relations by scalarization methods.First,we recall some linear and nonlinear scalarization prop-erties used to characterize the set order relations.Subsequently,we introduce new monotonicity concepts of the set-valued mapping by linear and nonlinear scalarization methods.Finally,we obtain the semicontinuity and closedness of solution mappings for parametric set optimization problems(both convex and nonconvex cases)under the monotonicity assumption and other suitable conditions.The results achieved do not impose the continuity of the set-valued objective mapping,which are obviously different from the related ones in the literature.展开更多
基金This research was supported by the National Natural Science Foundation of China(Nos.11301567 and 11571055)the Fundamental Research Funds for the Central Universities(No.106112017CDJZRPY0020).
文摘The aim of this paper is to investigate the continuity of solution mappings for para-metric set optimization problems with upper and lower set less order relations by scalarization methods.First,we recall some linear and nonlinear scalarization prop-erties used to characterize the set order relations.Subsequently,we introduce new monotonicity concepts of the set-valued mapping by linear and nonlinear scalarization methods.Finally,we obtain the semicontinuity and closedness of solution mappings for parametric set optimization problems(both convex and nonconvex cases)under the monotonicity assumption and other suitable conditions.The results achieved do not impose the continuity of the set-valued objective mapping,which are obviously different from the related ones in the literature.
