Key points are not available for this paper at this time.
Abstract Monotonicity implies the function's constant increase or non-negativity of its derivative. This article reviews 3 approaches to provide non-negativity in function recovery. One of them is placing a spline into a power of an exponent, which leads to either the need to linearize the function, or to use numerical methods in optimization. Another approach is to use non-negativity conditions (conditions are added at the spline knots), which leads to a quadratic programming problem. The article describes a method for restoring a function from various functionals: the values themselves, the values of the first and second derivatives, definite integrals. The spline is represented in terms of values and second derivative values. A penalty for the measure of curvature is also used. Examples of the method's application are demonstrated, and a software implementation of the method in Python is provided. Providing monotony with exponential approach uses standard Python scipy package optimization tools. Providing monotonicity using quadratic programming involves either: 1) linear complementarity problem, which solved using the Lemke algorithm, optimized with numba tools; 2) CVXOPT optimization package, which based on inner point method. An example of using collocation based on a monotone spline for forecasting economic events is also presented. Python code available on GitHub: https://github.com/YuAKorablev/FunctionalSmoothingSpline
Yuriy Korablev (Wed,) studied this question.