In the expression:

${\underset{\Omega}{\min}\left\|\beta A\Omega^{-1}B+C\right\|_{F}^{2}+tr(W\Omega^{-1}W^T)},$ s.t. ${tr(\Omega)=1, \Omega \ge 0}$, where any element of ${\Omega}$ is nonnegative.

How to solve the variable $\Omega$?

  • $\begingroup$ Does $\Omega \ge 0$mean that elements of $\Omega$ are nonnegative elementwise, or that $\Omega$ is positive semidefinite? $\endgroup$ – Mark L. Stone Jul 14 at 17:30
  • $\begingroup$ Are you minimizing that expression? You need to say so (edit the question). $\endgroup$ – Mark L. Stone Jul 14 at 18:35
  • $\begingroup$ yes, this is a minimization problem, and ${\Omega}$ is a symmetric matrix and any element of Ω is nonnegative. $\endgroup$ – tjufan Jul 14 at 23:54
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    $\begingroup$ There are many issues with this post, but if we can fix'em, it is an interesting question. Is $\Omega$ full or is there a fixed sparsity pattern? This looks like a sparse approximate inverse problem, and it is clear that if $\Omega$ is full then this is very expensive to solve. $\endgroup$ – Abdullah Ali Sivas Jul 15 at 0:25
  • $\begingroup$ Yes, in fact, ${\Omega \in R^{c \times c}}$ and ${\Omega}$ has the full rank. $\endgroup$ – tjufan Jul 15 at 0:43

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