I want to solve a group Lasso minimization problem with optimization variable matrix \mathbf{W} \in \mathcal{C}^{N\times M} when there is a square of norm expression in the objective function but according to the DCP rules I can not use the square function of a norm operation (it gives a DCP error). How do we handle this problem in CVX since there are lots of optimization problem that they deal with square of norm?

Here is my objective function :

minimize ||\mathbf{HW-I_M}||_F^2+\sum_{i=1}^N ||\mathbf{w}_i||_2,

where $\mathbf{w}_i$s are the rows of \mathbf{W} and \mathbf{H} \in \mathcal{C}^{M\times N}.

currently I wrote the problem in Matlab as follows but I can not square the first norm expression.

%

cvx_begin

i=N;

j=M;

variable w(i,j) complex;

minimize( norm(H*w-I,‘fro’) + \lambda .*sum( norms(w,2,2) ) );

cvx_end

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