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$$\min_{X,P} \| X D + (P X P') \, D_0 \|_{\text{F}}$$

where $X$ is a symmetric matrix and $P$ is a permutation matrix. $D$ and $D_0$ are given symmetric matrices. Is there some way to solve this problem? Adding some other constraints may also be allowed.

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    $\begingroup$ What is a costant matrix? $\endgroup$
    – Henry.L
    Commented Apr 12, 2017 at 12:48
  • $\begingroup$ Sorry for my typo, I mean they are constant. $\endgroup$
    – Nolan
    Commented Apr 12, 2017 at 13:36
  • $\begingroup$ How big are the matrices? $\endgroup$
    – Rodrigo de Azevedo
    Commented Apr 13, 2017 at 7:25
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    $\begingroup$ What is the background? Motivation? Context? Where does this come from? $\endgroup$
    – Rodrigo de Azevedo
    Commented Apr 13, 2017 at 8:00

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