International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 11, Pages 1693-1711

Global and local optimality conditions in set-valued optimization problems

M. Durea

Faculty of Mathematics, “Alexandru Ioan Cuza” University of Iaşi, Boulevard Carol I, no.11, Iaşi 700506, Romania

Received 6 September 2004; Revised 18 April 2005

Copyright © 2005 M. Durea. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider both global and local conditions for optimization problems governed by set-valued maps. For global conditions, we present a comparative study and then we impose the weaker ones to obtain optimality conditions. Therefore, we introduce some local conditions and we prove that these conditions are useful (mainly) in the study of Borwein proper minima for the considered problems.