JNCA: On derivatives of set-valued maps and optimality conditions for set optimization



	Volume 10, Number 1, April 2009, pp. 41-50
Daishi Kuroiwa
Key words:
Set-valued map, directional derivative, set optimization, optimality condition, convex, pseudoconvex
Mathematices Subject Classification: 50C60, 90C48


	Abstract:
	We consider a set-valued optimization problem, which is an optimization problem with a set-valued objective map. We know that there are two types of criteria for solutions of the problem, one is the criterion of vector optimization and the other is the criterion of set optimization. In this paper, we consider a set optimization problem and investigate first order optimality conditions by using directional derivatives based on an embedding idea. Also we observe optimality conditions when the object set-valued map satisfies certain convexity assumptions.

On derivatives of set-valued maps and optimality conditions for set optimization