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Calculus for parabolic second-order derivatives

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Abstract

In this paper, a calculus for two second-order directional derivatives is presented and then applied in the development of second-order necessary optimality conditions for a nonsmooth mathematical program. The formulae of this calculus, which include rules for sums, pointwise maxima, and certain compositions of functions, are valid for a large class of non-Lipschitzian functions and in fact subsume the sharpest results of the calculus of first-order upper and lower epiderivatives. Two methods are utilized in the derivation of these formulae. One centers around the concept of metric regularity, while the other relies upon the use of recession cones and ‘interior tangent sets’.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Miami University, 45056, Oxford, OH, USA

    Doug Ward

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  1. Doug Ward
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Ward, D. Calculus for parabolic second-order derivatives. Set-Valued Anal 1, 213–246 (1993). https://doi.org/10.1007/BF01027635

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