Well, there’s this thread, plus Prescribing tolerance for positivedefiniteness , which you started.
And as I mentioned earlier in this thread, you can use MOSEK as solver under CVX with non-default tolerance
cvx_solver_settings('MSK_DPAR_INTPNT_CO_TOL_PFEAS',1e-12)
I don’t think I’d try to go smaller than that. This might not normally be recommended, but I think it can result in a tighter tolerance of min eigenvalue on semidefinite constraints. Feel free to try it and experiment.
https://docs.mosek.com/9.0/rmosek/parameters.html
MSK_DPAR_INTPNT_CO_TOL_PFEAS
Primal feasibility tolerance used by the interior-point optimizer for conic problems.
Default:
1.0e-8
Accepted:
[0.0; 1.0]