  The Douglas-Rachford and Peaceman-Rachford algorithms have been successfully
employed to solve convex optimization problems, or more generally find zeros of
monotone inclusions. Recently, the behaviour of these methods in the
inconsistent case, i.e., in the absence of solutions has triggered significant
consideration. It has been shown that under mild assumptions the shadow
sequence of the Douglas-Rachford algorithm converges weakly to a generalized
solution when the underlying operators are subdifferentials of proper lower
semicontinuous convex functions. However, no convergence behaviour has been
proved in the case of Peaceman-Rachford algorithm. In this paper, we prove the
convergence of the shadow sequences associated with the Douglas-Rachford
algorithm and Peaceman-Rachford algorithm when one of the operators is
uniformly monotone and $3^*$ monotone but not necessarily a subdifferential.
Several examples illustrate and strengthen our conclusion. We carry out
numerical experiments using example instances of optimization problems.
