Abstract
Just as first-order directional derivatives can be associated with concepts of tangent cone, so second-order directional derivatives of parabolic type can be naturally and profitably associated with second-order tangent sets. In this paper, a chain rule is presented for second-order directional derivatives whose corresponding tangent sets satisfy a short list of properties. This chain rule subsumes and sharpens previous results from the calculus of first- and second-order directional derivatives. Corollaries include second-order necessary optimality conditions for nondifferentiable programs.
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