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Least squares problem with left and right unknowns

For $i=1,...,n$, let $b_i$ be a scalar and $A_i$ be an $k\times l$ matrix. Is there a closed form solution for the following problem assuming $n>k+l$? $$\min_{x\in \mathbb{R}^k ,y\in \mathbb{R}^l} \...
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