A chain rule for first- and second-order epiderivatives and hypoderivatives |
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| Authors: | D.E. Ward |
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| Affiliation: | Department of Mathematics and Statistics, Miami University, Oxford, OH 45056, USA |
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| Abstract: | A chain rule is established for contingent and adjacent epiderivatives and hypoderivatives of compositions g○h, where h is assumed to be Hadamard directionally differentiable. Corollaries include a formula for the contingent and adjacent cones of an equality constraint set defined by a Hadamard directionally differentiable function. An analogous chain rule for second-order contingent and adjacent epiderivatives and hypoderivatives is also developed. |
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| Keywords: | Contingent cone Adjacent cone Epiderivative Hypoderivative Hadamard directional derivative Second-order tangent set Basic normal cone |
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