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Given points $p_1, \dots, p_n$ in $\mathbb{R}^d$, how do we find a point $x$ which maximizes $\frac{1}{n} \sum_{i=1}^n e^{-\|p_i - x\|^2}$? In other words, how do we find the maximizing point, or mode of a Gaussian kernel density estimation (KDE) centered at $p_1, \dots, p_n$? Given the power of KDEs in representing probability distributions and other continuous functions, the basic mode finding problem is widely applicable.
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