EDB — 198

Exercises

1. [198] Topics:Distance function, convex sets. Prerequisites:[0R9]↺↻,[19C]↺↻.Let \(A⊂ ℝ^ n\) be a closed nonempty set, and \(d_ A\) the distance function defined in the exercise [0R9]↺↻, that is \(d_ A(x)=\inf _{y∈ A} |x-y|\). Prove that \(A\) is a convex set, if and only if \(d_ A\) is a convex function.

   Solution 1

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