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SOOCHOW JOURNAL OF MATHEMATICS

Volume 33, No. 4, pp. 629-640, October 2007




SUPER EFFICIENCY IN VECTOR OPTIMIZATION

PROBLEMS WITH IC-CONE-CONVEXLIKE

SET-VALUED MAPS


BY


GUO-LIN YU AND HONG-AN ZHOU




Abstract. This paper gives an useful property of ic-cone-convexlike set-valued maps. By using this property as the main tool, the scalarization theorem and optimality conditions for super efficient solutions of a vector optimization problem with the ic-cone-convexlike objectives and constraints in normed linear spaces are proposed. In addition, it shows that a super efficient solution can be expressed in terms of saddle point.

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Received October 19, 2005; revised May 24, 2007.

AMS Subject Classification. Primary 90C29, 90C46; scondary 49K27, 49C25.

Key words. set-valued optimization, super efficiency, ic-cone-convexlikeness, optimality conditions, saddle point.

This research is supported by National Science Foundation of China under Grant No. 60674708, P. R. China.