Yes, try to get the elements of `H’ to be close to magnitude 1.
I think that you need adequate scaling of everything else so that 1e-5, or maybe 1e-6 is adequate to ensure you get the strict nonnegativity you need in that constraint… Your other option is to adjust the solution from CVX prior to feeding them into your next iteration.
If you use SCA. there may be a risk that even if the 1st SCA iteration is well-scaled, some later iteration may not be. See