Shogo Nishizawa, Maki Onodsuka and Tamaki Tanaka
	Key words:		alternative theorem, nonlinear scalarization, vector optimization,
set-valued optimization, set-valued maps, optimality conditions
Mathematices Subject Classification: 90C29, 90C46, 49J53

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	Abstract:
			Based on a comparison of a set with the zero vector with respect to a
		given convex cone, we establish five types of alternative theorems for set-valued maps without any convexity assumption, which are proved by a nonlinear scalarization technique. As an application, we obtain optimality conditions for vector optimization problems with set-valued maps.

Alternative theorems for set-valued maps based on a nonlinear scalarization

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Special Issue in Honor of the 70th Birthday of R.Tyrrell Rockafellar
Volume 1, Number 1, January 2005, pp. 147-159