  In the past decade, we had developed a series of splitting contraction
algorithms for separable convex optimization problems, at the root of the
alternating direction method of multipliers. Convergence of these algorithms
was studied under specific model-tailored conditions, while these conditions
can be conceptually abstracted as two generic conditions when these algorithms
are all unified as a prediction-correction framework. In this paper, in turn,
we showcase a constructive way for specifying the generic
convergence-guaranteeing conditions, via which new splitting contraction
algorithms can be generated automatically. It becomes possible to design more
application-tailored splitting contraction algorithms by specifying the
prediction-correction framework, while proving their convergence is a routine.
