I have a question, Suppose $ A, B, D \in \mathbb{R}^{n \times p} $, I want to solve the following optimization problem:

$\arg\min_D\frac{1}{2}\|D + A\|_F^2 + \lambda\|BB^T + DB^T + BD^T\|_1 \mbox{ s.t. } D^TB + B^TD = 0, B^TB = I_p$.

We can view that $D$ is on the tangent space of Stiefel Manifold.

Do you guys have any idea on how to solve that?

Thanks a lot!


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