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The stability of the solution sets for set optimization problems via improvement sets. (English) Zbl 1427.49012

Summary: The aim of this paper is to investigate the stability of the solution sets for set optimization problems via improvement sets. Firstly, we consider the relations among the solution sets for optimization problem with set optimization criterion. Then, the closeness and the convexity of solution sets are discussed. Furthermore, the upper semi-continuity, Hausdorff upper semi-continuity and lower semi-continuity of solution mappings to parametric set optimization problems via improvement sets are established under some suitable conditions. These results extend and develop some recent works in this field.

MSC:

49J45 Methods involving semicontinuity and convergence; relaxation
49J53 Set-valued and variational analysis
90C31 Sensitivity, stability, parametric optimization
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