Given a set $F$ of $n$ positive functions over a ground set $X$, we consider the problem of computing $x^*$ that minimizes the expression $\sum_{f\in F}f(x)$, over $x\in X$. A typical application is \emph{shape fitting}, where we wish to approximate a set $P$ of $n$ elements (say, points) by a shape $x$ from a (possibly infinite) family $X$ of shapes... (read more)

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