The set-valued optimization problem minC F(x), G(x)∩(−K) = ∅, is considered, where F : Rn Rm and G : Rn Rp are set-valued functions, and C ⊂ Rm and K ⊂ Rp are closed convex cones. Two type of solutions, called w-minimizers (weakly efficient points) and i-minimizers (isolated minimizers), are treated. In terms of the Dini set-valued directional derivative first-order necessary conditions for a point to be a w-minimizer, and first-order sufficient conditions for a point to be an i-minimizer are established, both in primal and dual form.
On constrained set-valued optimization
IVANOV, IVAN GINCHEV;
2007-01-01
Abstract
The set-valued optimization problem minC F(x), G(x)∩(−K) = ∅, is considered, where F : Rn Rm and G : Rn Rp are set-valued functions, and C ⊂ Rm and K ⊂ Rp are closed convex cones. Two type of solutions, called w-minimizers (weakly efficient points) and i-minimizers (isolated minimizers), are treated. In terms of the Dini set-valued directional derivative first-order necessary conditions for a point to be a w-minimizer, and first-order sufficient conditions for a point to be an i-minimizer are established, both in primal and dual form.
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