Dept. of Mathematical Sciences, Univ. of Alberta, Edmonton, Alberta, T6G 2G1, Canada, rene.poliquin@ualberta.ca, and Dept. of Mathematics, Univ. of Washington, Seattle, WA 98195, USA, rtr@math.washington.edu
Abstract: Partial subgradient mappings have a key role in the sensitivity analysis of first-order conditions for optimality, and their generalized derivatives are especially important in that respect. It is known that such a mapping is proto-differentiable when it comes from a fully amenable function with compatible parameterization, which is a common case in applications; the proto-derivatives can be evaluated then through projections. Here this result is extended to a still broader class of functions than fully amenable, namely, ones obtained by composing a $C^2$ mapping with a kind of piecewise-$C^2$ convex function under a constraint qualification.
Keywords: Variational analysis, subgradient mappings, proto-derivatives, second-order epi-derivatives, amenable functions, piecewise-$C^2$ functions, nonsmooth analysis
Classification (MSC2000): 49A52, 58C06, 58C20; 90C30
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