how to adopt a DC representation for the rank-one constraint.(W_{0})is a PSD matrix and(\mathrm{T}\mathrm{r}(W_{0})>0.

\begin{align*}&minimize \mathrm{T}\mathrm{r}(W_{0})+\rho(\mathrm{T}\mathrm{r}(W_{0})-\Vert W_{0}\Vert_{2})w_{0},{W_{k}}\&+\sum_{k=1}^{K}\mathrm{T}\mathrm{r}(W_{k})+\rho\sum_{k=1}^{K}(\mathrm{T}\mathrm{r}(W_{k})-\Vert W_{k}\Vert_{2}) \tag{10a}\end{align*}

and how to use the majorization-minimization technique

\begin{align*}\operatorname{minimize} & \operatorname{Tr}\left(W_{0}\right)+\rho\left(\left\langle W_{0}, I-\partial_{W_{0}^{t-1}}\left|W_{0}\right|*{2}\right\rangle\right) \W*{0},\left{W_{k}\right} &+\sum_{k=1}^{K} \operatorname{Tr}\left(W_{k}\right)+\rho \sum_{k=1}^{K}\left(\left\langle W_{k}, I-\partial_{W_{k}^{t-1}}\left|W_{k}\right|_{2}\right\rangle\right)\& \text{subject to Constraints} (6 b), (6 c), (6 d), \tag{11a}\end{align*}

in CVX

The trace norm is another name for nuclear norm, which is available in CVX as `norm_nuc`

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How to to DC representations and how to use the majorization-minimization technique are out of scope of this forum.

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