| Article ID: | iaor20172804 |
| Volume: | 68 |
| Issue: | 4 |
| Start Page Number: | 899 |
| End Page Number: | 923 |
| Publication Date: | Aug 2017 |
| Journal: | Journal of Global Optimization |
| Authors: | Durea Marius |
| Keywords: | heuristics, sets |
In this paper we use a double penalization procedure in order to reduce a set‐valued optimization problem with functional constraints to an unconstrained one. The penalization results are given in several cases: for weak and strong solutions, in global and local settings, and considering two kinds of epigraphical mappings of the set‐valued map that defines the constraints. Then necessary and sufficient conditions are obtained separately in terms of Bouligand derivatives of the objective and constraint mappings.