Limiting subhessians, limiting subjets and their calculus

Ioffe, Alexander; Penot, Jean-Paul

doi:10.1090/S0002-9947-97-01726-1

Limiting subhessians, limiting subjets and their calculus
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by Alexander D. Ioffe and Jean-Paul Penot PDF

Trans. Amer. Math. Soc. 349 (1997), 789-807 Request permission

Abstract:

We study calculus rules for limiting subjets of order two. These subjets are obtained as limits of sequences of subjets, a subjet of a function $f$ at some point $x$ being the Taylor expansion of a twice differentiable function which minorizes $f$ and coincides with $f$ at $x$. These calculus rules are deduced from approximate (or fuzzy) calculus rules for subjets of order two. In turn, these rules are consequences of delicate results of Crandall-Ishii-Lions. We point out the similarities and the differences with the case of first order limiting subdifferentials.

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