  We consider Schr\"odinger operators with complex-valued decreasing potentials
on the half-line. Such operator has essential spectrum on the half-line plus
eigenvalues (counted with algebraic multiplicity) in the complex plane without
the positive half-line. We determine trace formula: sum of Im part of these
eigenvalues plus some singular measure plus some integral from the Jost
function. Moreover, we estimate of sum of Im part of eigenvalues and singular
measure in terms of the norm of potentials. In addition, we get bounds on the
total number of eigenvalues, when the potential is compactly supported.
