In terms of the Slater condition of the Bouligand and Clarke tangent derivatives of the objective multifunction Ψ,this paper mainly studies the stability of error bound of Ψ at a point x with respect to an ordering cone C.It is proved that the Slater condition of the Bouligand tangent derivative of Ψ at x with respect to C is always stable with respect to all small calm perturbations.Based on this result,we prove that the Slater condition of the Bouligand tangent derivative of Ψ at x with respect to C is a sufficient condition for Ψ to have a stable error bound at x with respect to C when Ψ undergoes small calm and regular perturbations.These results extend the corresponding ones given by Zheng[Math Oper Res,2022,47(4):3282-3303]from the vector-valued to the set-valued case.As applications,some sufficient conditions are provided for a convex progress to have a stable global error bound with respect to an ordering cone.
维普
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