Abstract
Hern\(\acute{\mathrm{a}}\)ndez and Rodríguez-Marín (J Math Anal Appl 325:1–18, 2007) introduced a nonlinear scalarizing function for sets, which is a generalization of the Gerstewitz’s function. This paper aims at investigating some properties concerned with the nonlinear scalarizing function for sets. The continuity and convexity of the nonlinear scalarizing function for sets are showed under some suitable conditions. As applications, the upper semicontinuity and the lower semicontinuity of strongly approximate solution mappings to the parametric set optimization problems are also given.
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The authors are grateful to the editor and the referees for their valuable comments and suggestions. This work was supported by the National Natural Science Foundation of China (11471230, 11671282).
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Han, Y., Huang, Nj. Continuity and Convexity of a Nonlinear Scalarizing Function in Set Optimization Problems with Applications. J Optim Theory Appl 177, 679–695 (2018). https://doi.org/10.1007/s10957-017-1080-9
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DOI: https://doi.org/10.1007/s10957-017-1080-9