I believe the essence of the situation is your need to express the following construct in CVX:

`x1*log(x1)+x2*log(x2) - (x1+x2)*log(x1+x2)`

This can be re-written as

```
x1*(log(x1) - log(x1+x2)) + x2*(log(x2) - log(x1+x2)) =
x1*log(x1/(x1+x2)) + x2*log(x2/(x1+x2)) =
rel_entr(x1,x1+x2) + rel_entr(x2,x1+x2)
```

I’ll let you extend this in the obvious way to your matrix variable and summation.

Thank you for your quick response and your great help! I will try to use this now. Thanks again !