Continuity of solutions mappings of parametric set optimization problems

Abstract

<p style='text-indent:20px;'>Set optimization is an indispensable part of theory and method of optimization, and has been received wide attentions due to its extensive applications in group decision and group game problems. This paper focus on the continuity of the strict (weak) minimal solution set mapping of parametric set-valued vector optimization problems with the lower set less order relation. We firstly introduce a concept of strict lower level mapping of parametric set-valued vector optimization problems. Moreover, the upper and lower semicontinuity of the strict lower level mapping are obtained under some suitable conditions. Lastly, the sufficient condition for the continuity of the strict minimal solution set mappings of parametric set optimization problems are established by a new proof method, which is different from that in [<xref ref-type="bibr" rid="Xu2014">27</xref>,<xref ref-type="bibr" rid="Xu2016">28</xref>].