Epi-convergence Properties of Smoothing by Infimal Convolution |
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Authors: | James V. Burke Tim Hoheisel |
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Affiliation: | 1.Department of Mathematics,University of Washington,Seattle,USA;2.Institute of Mathematics, Campus Hubland Nord,University of Würzburg,Würzburg,Germany |
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Abstract: | This paper concerns smoothing by infimal convolution for two large classes of functions: convex, proper and lower semicontinous as well as for (the nonconvex class of) convex-composite functions. The smooth approximations are constructed so that they epi-converge (to the underlying nonsmooth function) and fulfill a desirable property with respect to graph convergence of the gradient mappings to the subdifferential of the original function under reasonable assumptions. The close connection between epi-convergence of the smoothing functions and coercivity properties of the smoothing kernel is established. |
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