I have to minimize w1ObjA(X) + w2ObjB(X) to get X. I used the SDP with the CVX package for the resolution. When w1 is chosen be very small (10^-13) and w2=1. The minimization gave us good results.
The same things (same results) are happened when w1=0, which is unexpectable.
However, when we have completely removed the first term and we have minimized only w2*ObjB(X), we did not have the same results. Instead, we obtained bad performance, which is expectable for our case.
When we put w=0, did the SDP with the CVX package continue considering the first term when resolving w1ObjA(X) + w2ObjB(X) ?? I think that it all depends on how the procedure works internally.
Thank you in advance.