Minimizing $|AYGG^TY^T-B|_F^2$ subject to $G^TG=I_r$
Let $A$ and $B$ belong to $mathbb{R}^{ptimes n}$ and $Yin mathbb{R}^{ntimes d}$ with orthonormal columns (i.e., $Y^T Y = I_d$). How can I solve the following optimization problem?
begin{eqnarray}
&&min_{G} |A Y G G^T Y^T -B|_F^2\
&&mathrm{subject to} G^T G = I_r,
end{eqnarray}
where $Gin mathbb{R}^{dtimes r}$ and $|cdot|_F$ is Frobenius norm.
Note that $G G^T$ and $Y G G^T Y^T$ are projection matrices.
linear-algebra optimization
asked 2 days ago
Bashir SadeghiBashir Sadeghi
324
add a comment |
Let $A$ and $B$ belong to $mathbb{R}^{ptimes n}$ and $Yin mathbb{R}^{ntimes d}$ with orthonormal columns (i.e., $Y^T Y = I_d$). How can I solve the following optimization problem?
begin{eqnarray}
&&min_{G} |A Y G G^T Y^T -B|_F^2\
&&mathrm{subject to} G^T G = I_r,
end{eqnarray}
where $Gin mathbb{R}^{dtimes r}$ and $|cdot|_F$ is Frobenius norm.
Note that $G G^T$ and $Y G G^T Y^T$ are projection matrices.
linear-algebra optimization
asked 2 days ago
Bashir SadeghiBashir Sadeghi
324
You're right. I'll delete the comment.
– mathcounterexamples.net
2 days ago
add a comment |
Let $A$ and $B$ belong to $mathbb{R}^{ptimes n}$ and $Yin mathbb{R}^{ntimes d}$ with orthonormal columns (i.e., $Y^T Y = I_d$). How can I solve the following optimization problem?
begin{eqnarray}
&&min_{G} |A Y G G^T Y^T -B|_F^2\
&&mathrm{subject to} G^T G = I_r,
end{eqnarray}
where $Gin mathbb{R}^{dtimes r}$ and $|cdot|_F$ is Frobenius norm.
Note that $G G^T$ and $Y G G^T Y^T$ are projection matrices.
linear-algebra optimization
asked 2 days ago
Bashir SadeghiBashir Sadeghi
324
Let $A$ and $B$ belong to $mathbb{R}^{ptimes n}$ and $Yin mathbb{R}^{ntimes d}$ with orthonormal columns (i.e., $Y^T Y = I_d$). How can I solve the following optimization problem?
begin{eqnarray}
&&min_{G} |A Y G G^T Y^T -B|_F^2\
&&mathrm{subject to} G^T G = I_r,
end{eqnarray}
where $Gin mathbb{R}^{dtimes r}$ and $|cdot|_F$ is Frobenius norm.
Note that $G G^T$ and $Y G G^T Y^T$ are projection matrices.
linear-algebra optimization
linear-algebra optimization
asked 2 days ago
Bashir SadeghiBashir Sadeghi
324
asked 2 days ago
Bashir SadeghiBashir Sadeghi
324
edited 2 days ago
Bashir Sadeghi
asked 2 days ago
Bashir SadeghiBashir Sadeghi
324
asked 2 days ago
Bashir SadeghiBashir Sadeghi
324
asked 2 days ago
Bashir SadeghiBashir Sadeghi
324
324
You're right. I'll delete the comment.
– mathcounterexamples.net
2 days ago
add a comment |
You're right. I'll delete the comment.
– mathcounterexamples.net
2 days ago
You're right. I'll delete the comment.
– mathcounterexamples.net
2 days ago
You're right. I'll delete the comment.
– mathcounterexamples.net
2 days ago
add a comment |
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You're right. I'll delete the comment.
– mathcounterexamples.net
2 days ago