Consider a permutation matrix $P$ and two vectors $x$, $v$ with 2-norm = 1 and all positive entries.
Are the optimal solutions $P^\ast$ of $\max_P \; (x^T \cdot Py)$ and $\min_P \; \|x-Py\|_2$ the same?
\|x-Py\|_2^2=\|x\|_2^2+\|Py\|_2^2-2x^T\cdot Py=2(1-x^T\cdot Py)
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4 years ago
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