Hi @rpetit,
Take a read of Tolerances and numerical issues · JuMP
You cannot reasonably expect Mosek to find a solution to a tolerance of 1e-14. Is there anything earlier in the log warning about the tolerances being too tight?
You might also be interested in https://www.blogger.com/blogger.g?blogID=2124323532937076865#overview The MOSEK blog: Should Mosek optimizer parameters be tweaked?