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Limiting subhessians, limiting subjets and their calculus |
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| Authors: | Alexander D. Ioffe Jean-Paul Penot |
| Affiliation: | Department of Mathematics, Technion, 32000 Haifa, Israel Jean-Paul Penot ; Départment de Mathématiques, CNRS URA 1204, Faculté des Sciences, Av. de l'Université, 64000 Pau, France |
| 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  at some point  being the Taylor expansion of a twice differentiable function which minorizes  and coincides with  at  . 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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