Based on near convexity, we introduce the concepts of nearly convexlike set-valued maps and nearly semiconvexlike set-valued maps, give some charaterizations of them, and investigate the relationships between them. Then a Farkas-Minkowski type alternative theorem is shown under the assumption of near semiconvexlikeness. By using the alternative theorem and some other lemmas, we establish necessary optimality conditions and sufficient optimality conditions for set-valued vector optimization with extended inequality constraints in a sense of weak E-minimizers.
March, 2002 The Chinese University of Hong Kong, Department of Systems Engineering and Engineering Management, Shatin, NT, Hong Kong.
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