Continuity and convexity of a nonlinear scalarizing function in set optimization problems with applications
The first part of the paper contains necessary continuity concepts of set-valued mappings and introduces the Gerstewitz's function. In the next part, properties of the nonlinear scalarizing function are studied. The nonlinear scalarizing function is a generalization of Gerstewithz's function introduced by \textit{E. Hernández} and \textit{L. Rodríguez-Marín} [J. Math. Anal. Appl. 325, No. 1, 1--18 (2007; Zbl 1110.90080)]. The main results of the paper consist in conditions, under which continuity and convexity of the nonlinear scalarizing function can be proved. ``The results are applied to proving the upper and lower semicontinuity of strongly approximate solution mappings to the parametric set optimization problems''.
scientific article; zbMATH DE number 6931974
scientific article