Optimization is the process of choosing the "best" value among possible values. They are often formulated as questions on the minimization/maximization of functions, with or without constraints.

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Are any tools or techniques available to solve the “placement of safety points” problem?

Definition 0. Given a metric space $X$ and subsets $H$ and $S$ thereof, define: $$d(H,S) = \sup_{h \in H} \inf_{s \in S}d(h,s)$$ Here's some slightly dodgy intuition. Imagine $S$ is a set of ...