Second Order Subdifferentials Constructed Using Integral Convolutions Smoothing
In this paper we demonstrate that second order subdifferentials constructed via the accumulation of local Hessian information provided by an integral convolution approximation of the function, provide useful information only for a limited class of nonsmooth functions. When local finiteness of associated second order directional derivative is demanded this forces the first order subdifferential to possess a local Lipschitz property. To enable the study of a broader classes of nonsmooth functions we show that a combination of the infimal and integral convolutions needs to be used when constructing approximating smooth functions.
KeywordsSecond order Subdifferentials integral convolution infimal convolution
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