Minimizing $|AYGG^TY^T-B|_F^2$ subject to $G^TG=I_r$












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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







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  • $begingroup$
    You're right. I'll delete the comment.
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    Jan 5 at 15:39
















0












$begingroup$


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







share|cite|improve this question











$endgroup$












  • $begingroup$
    You're right. I'll delete the comment.
    $endgroup$
    – mathcounterexamples.net
    Jan 5 at 15:39














0












0








0





$begingroup$


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







share|cite|improve this question











$endgroup$




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






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Jan 5 at 16:18







Bashir Sadeghi

















asked Jan 5 at 14:59









Bashir SadeghiBashir Sadeghi

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  • $begingroup$
    You're right. I'll delete the comment.
    $endgroup$
    – mathcounterexamples.net
    Jan 5 at 15:39


















  • $begingroup$
    You're right. I'll delete the comment.
    $endgroup$
    – mathcounterexamples.net
    Jan 5 at 15:39
















$begingroup$
You're right. I'll delete the comment.
$endgroup$
– mathcounterexamples.net
Jan 5 at 15:39




$begingroup$
You're right. I'll delete the comment.
$endgroup$
– mathcounterexamples.net
Jan 5 at 15:39










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