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The Optimality Condition of Henig Proper Efficiency for a Set-Valued Optimization Problem

In locally convex topological space, by applying the Assumption (C) which is weaker than the generalized slater constraint condition, we have studied the Lagrange and Kuhn-Tucker type optimality condition for the Henig proper efficiency of the ic-cone-convex like set-valued optimization problem. And meanwhile all the results obtained in this paper are proven under the conditions that the constraint cone need not to have a closed convex bounded base.