Abstract
We study the connexion between local and global decompositions of some important subclasses of locally d.c. functions (functions which locally split as a difference of two convex functions). Then we tackle the problem of regularizing such functions by the Moreau-Yosida process and prove in particular that the class of lower-C 2 functions fits well this approximation procedure.
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Penot, J.P., Bougeard, M.L. Approximation and decomposition properties of some classes of locally D.C. functions. Mathematical Programming 41, 195–227 (1988). https://doi.org/10.1007/BF01580764
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DOI: https://doi.org/10.1007/BF01580764