Let A \in \mathbf{R}^{kD \times D}, Q \in \mathbf{R}^{D \times D}, where A is fixed, Q is unknown, k=2 and D=256. The objective is

My direct translation to CVX is

```
oneskd = ones(k*D,1);
onesd = ones(D,1);
cvx_begin
variable Q(D,D);
minimise ( norm(oneskd - A*Q*onesd,1) );
A*Q >= 0;
cvx_end
```

The result is a model with 198144 variables and 131584 equality constraints. Now, in practical applications k is larger than 2, e.g. in the area of 20, or so. However, even with k=2 it already takes more than 8 minutes to solve. Converting the above problem into an equivalent LP did not really help.

Any suggestions how to improve runtime? Whilst A and Q are not sparse, the product AQ should be sparse - not sure if this helps…