A note on semicontinuity of the solution mapping for parametric set optimization problems

The present work is devoted to studying the stability of a parametric set optimization problem. In particular, based on the partial order relation on the family of nonempty bounded sets defined by Karaman et al. (Positivity 22(3):783–802, 2018), we give some sufficient conditions for the upper semicontinuity, lower semicontinuity, and closedness of the solution mapping to a parametric set optimization problem.

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