I have specified a problem whose objetive function comprises a norm error cost function to be minimized subject to LMI constraints.

minimize norm (error)

subject to LMI ==semidefinite

CVX does solve the problem with an excelent fit to the data but there seems to be some very small negative (something of the magnitude -1e^-7) eigenvalues which violate the constraints.

Is there a way to require cvx not to allow for negative eigenvalues? So to speak could I raise the tolerance to some small but positive eigenvalue, say +1e^-7?