  The problem of monotone smoothing splines with bounds is formulated as a
constrained minimization problem of the calculus of variations. Existence and
uniqueness of solutions of this problem is proved, as well as the equivalence
of it to a finite dimensional but nonlinear optimization problem. A new
algorithm for computing the solution which is a spline curve, using a branch
and bound technique, is presented. The method is applied to examples in
neuroscience and for fitting cumulative distribution functions from data.

Optimization and Control