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Second-order lower radial tangent derivatives and applications to set-valued optimization
Bihang Xu1, Zhenhua Peng2, Yihong Xu3
1School of Information Engineering, Nanchang University, Nanchang, 330031 China.
Abstract:
We introduce the concepts of second-order radial composed tangent derivative, second-order radial tangent derivative, second-order lower radial composed tangent derivative, and second-order lower radial tangent derivative for set-valued maps by means of a radial tangent cone, second-order radial tangent set, lower radial tangent cone, and second-order lower radial tangent set, respectively. Some properties of second-order tangent derivatives are discussed, using which second-order necessary optimality conditions are established for a point pair to be a Henig efficient element of a set-valued optimization problem, and in the expressions the second-order tangent derivatives of the objective function and the constraint function are separated.
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