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Keywords:
distance function; DC function; subset of ${\mathbb R}^2$
distance function; DC function; subset of ${\mathbb R}^2$
Summary:
We give a complete characterization of closed sets $F \subset {\mathbb R}^2$ whose distance function $d_F:= {\rm dist}(\cdot ,F)$ is DC (i.e., is the difference of two convex functions on ${\mathbb R}^2$). Using this characterization, a number of properties of such sets is proved.
References:
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