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Approximation and decomposition properties of some classes of locally d.c. functions. (English) Zbl 0666.49005
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.

MSC:
49J52 Nonsmooth analysis
26B25 Convexity of real functions of several variables, generalizations
90C30 Nonlinear programming
49M27 Decomposition methods
90C55 Methods of successive quadratic programming type
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