SCALARIZATION AND SEMICONTINUITY OF APPROXIMATE SOLUTIONS TO SET OPTIMIZATION PROBLEMS

This paper deals with the approximate solutions to set optimization problems in the sense of strict upper set less order relation. First, the concept of scalar approximate solutions is introduced, and its relationship to the approximate weak minimal solutions is proposed. Second, by using the oriented distance function, a scalarization theorem is established for approximate weak minimal solutions. Finally, the upper and lower semicontinuity of approximate weak minimal solution mappings are proved for the parametric set optimization problems. © 2022 Applied Set-Valued Analysis and Optimization.