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I am encountering a constrained LS problem with the following structure: $$ \text{min}_Q\ \sum_{i=1}^M ||Q_i X_i-Y_i||_F^2 $$ $$ \text{s.t. }\ Q_M Q_{M-1}\cdots Q_1=I, $$ where $Q_i,X_i,Y_i\in \mathbb{R}^{n\times n}$ are full rank.

I understand this can be a very hard problem. I just want to know if there is a numerically converging algorithm for this type of problem by any chance.

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  • $\begingroup$ @FedericoPoloni Sorry, it should be a sum of squared norms, but $Q$ is not orthogonal. $\endgroup$
    – Yin Mingzhou
    Commented Mar 27, 2020 at 6:48

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