  Regression in supervised learning often requires the enforcement of
constraints to ensure that the trained models are consistent with the
underlying structures of the input and output data. This paper presents an
iterative procedure to perform regression under arbitrary constraints. It is
achieved by alternating between a learning step and a constraint enforcement
step, to which an affine extension function is incorporated. We show this leads
to a contraction mapping under mild assumptions, from which the convergence is
guaranteed analytically. The presented proof of convergence in regression with
constraints is the unique contribution of this paper. Furthermore, numerical
experiments illustrate improvements in the trained model in terms of the
quality of regression, the satisfaction of constraints, and also the stability
in training, when compared to other existing algorithms.
