  We perform a systematic study of the one-loop renormalization-group-improved
effective potential of the minimal supersymmetric extension of the Standard
Model (MSSM), including CP violation induced radiatively by soft trilinear
interactions related to squarks of the third generation. We calculate the
charged and neutral Higgs-boson masses and couplings, including the two-loop
logarithmic corrections that arise from QCD effects, as well as those
associated with the top- and bottom-quark Yukawa couplings. We also include the
potentially large two-loop non-logarithmic corrections induced by one-loop
threshold effects on the top- and bottom-quark Yukawa couplings, due to the
decoupling of the third-generation squarks. Within this minimal CP-violating
framework, the charged and neutral Higgs sectors become intimately related to
one another and therefore require a unified treatment. In the limit of a large
charged Higgs-boson mass, M_{H^+} >> M_Z, the lightest neutral Higgs boson
resembles that in the Standard Model (SM), and CP violation occurs only in the
heavy Higgs sector. Our analysis shows that sizeable radiative effects of CP
violation in the Higgs sector of the MSSM may lead to significant modifications
of previous studies for Higgs-boson searches at LEP2, the Tevatron and the LHC.
In particular, CP violation could enable a relatively light Higgs boson to
escape detection at LEP2.
