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Continuity of Solution Mappings for Parametric Set Optimization Problems under Partial Order Relations
College of Science, Chongqing University of Posts and Telecommunications, Chongqing, China
- 1 College of Science, Chongqing University of Posts and Telecommunications, Chongqing, China
Advances in Pure Mathematics·Volume 10 (2020)·Pages 631–644·Published 12 November 2020·DOI10.4236/apm.2020.1011039
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Abstract
This paper mainly investigates the semicontinuity of solution mappings for set optimization problems under a partial order set relation instead of upper and lower set less order relations. To this end, we propose two types of monotonicity definition for the set-valued mapping introduced by two nonlinear scalarization functions which are presented by these partial order relations. Then, we give some sufficient conditions for the semicontinuity and closedness of solution mappings for parametric set optimization problems. The results presented in this paper are new and extend the main results given by some authors in the literature.
KeywordsParametric Set Optimization ProblemNonlinear Scalarization FunctionSemicontinuityPartial Order Relation
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