  For the inclusion problem involving two maximal monotone operators, under the
metric subregularity of the composite operator, we derive the linear
convergence of the generalized proximal point algorithm and several splitting
algorithms, which include the over-relaxed forward-backward splitting
algorithm, the generalized Douglas-Rachford splitting algorithm and Davis'
three-operator splitting algorithm. To the best of our knowledge, this linear
convergence condition is weaker than the existing ones that almost all require
the strong monotonicity of the composite operator. Withal, we give some
sufficient conditions to ensure the metric subregularity of the composite
operator. At last, the preliminary numerical performances on some toy examples
support the theoretical results.
