| Article ID: | iaor20114196 |
| Volume: | 149 |
| Issue: | 2 |
| Start Page Number: | 352 |
| End Page Number: | 365 |
| Publication Date: | May 2011 |
| Journal: | Journal of Optimization Theory and Applications |
| Authors: | Hernndez Elvira, Rodrguez-Marn Luis |
| Keywords: | maps, subgradient methods |
We consider weak subgradients of a set‐valued map and present a new notion of strong subgradient. We study their properties and compare our constructions and results with other developments. We give existence conditions of both types and establish several optimality conditions in terms of set optimization.