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Monotone smoothing splines with bounds

Research paper by Sara Maad Sasane

Indexed on: 26 Nov '20Published on: 15 Sep '19Published in: arXiv - Mathematics - Optimization and Control



Abstract

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.