| A constrained optimization problem minC F(x), G(x) \cap (-K) ≠ \emptyset is considered, where X, Y, Z are normed spaces, F: X \sto Y , G : X \sto Z are set-valued functions and C and K are closed convex (not necessarily pointed) cones. The solutions of the set-valued problem are called minimizers. The notions of w-minimizers (weakly efficient points), p-minimizers (properly efficient points) and i-minimizers (isolated minimizers) are introduced. These notions are investigated and characterized by first order necessary and sufficient conditions given by means of a Dini derivative for set-valued maps. The case of convex-along-rays data is considered to have sufficient optimality conditions for weak minimizers. This paper generalizes [4] where an unconstrained set-valued optimization problem was considered. |
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