Abstract
By viewing jets as an inductive extension of the first order proximal analysis of loffe and Mordukhovich one is able to extend many constructs appearing in the first order theories to the second order case. We find that the second order Dini derivative is the rank one support of a set of matrices whose rank one representer coincides with the subjets. The rank one support plays a key role in this development as does the infimal convolution (or negative the Φ2-conjugate). Both of these concepts interact in unexpected ways. In particular we find that the infimal convolution smoothing of a function makes the subjet set more rotund (in a rank one sense). We also demonstrate a number of approximation theorems for subjets involving the infimal convolution.
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Eberhard, A., Nyblom, M., Ralph, D. (1998). Applying Generalised Convexity Notions to Jets. In: Crouzeix, JP., Martinez-Legaz, JE., Volle, M. (eds) Generalized Convexity, Generalized Monotonicity: Recent Results. Nonconvex Optimization and Its Applications, vol 27. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3341-8_4
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DOI: https://doi.org/10.1007/978-1-4613-3341-8_4
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