  In this paper, the analytic sufficient and necessary conditions are obtained
for the CP conserving two-Higgs-doublet potential to be bounded from below by
using the co-positivity of tensors. This is achieved by treating the potential
as a quartic homogeneous polynomial about the moduli of the two Higgs doublet
fields, where the 'angles' is described as the misalignment of the two
doublets, then solving three minimum problems with respect to the misalignment.
Finally, the analytic conditions are established with the help of the
corresponding theory and methods of higher order tensors.
