PJO: Duality in set optimization with set-valued maps



			Volume 3, Number 2, May 2007, pp. 245-255
			Elvira Hernández and Luis Rodríguez-Marín
			Key words:
		set-valued maps, set optimization, duality theory
Mathematices Subject Classification: 90C29, 90C46, 49N15
	References


	Abstract:
	A general optimization problem with set-valued maps is studied. The solution is taken in terms of the set optimization criterion due to D. Kuroiwa [11]. We introduce a dual problem by means a generalized Lagrangian, obtain weak and strong duality and establish a relation between the primal and the dual problem. Finally, a necessary optimality condition for minimality in set optimization is given through a multiplier rule of linear type.

Duality in set optimization with set-valued maps