## Complements, approximations, smoothings and invariance properties.(English)Zbl 0905.49010

Consider a closed nonempty set $$S$$ in the usual $$n$$-dimensional Euclidean space. Let $$x$$ be a point in $$S$$. The proximal normal cone to $$S$$ at $$x$$ is a geometric concept of great importance for the differentiability analysis of the boundary of $$S$$. The authors establish some links between proximal normal cones to $$S$$ and proximal normal cones to the closure of the complement of $$S$$. As an application of the general “complementary proximal normal formula”, the authors obtain some invariance properties for a class of differential inclusions.
Reviewer: A.Seeger (Avignon)

### MSC:

 49J52 Nonsmooth analysis 26B05 Continuity and differentiation questions

### Keywords:

proximal normal cone; differential inclusions
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