An Efficient Algorithm for Generating Univariate Cubic L1 Splines

Authors:
Hao Cheng;Shu-Cherng Fang;John E. Lavery
Affiliations:
Industrial Engineering and Operations Research, North Carolina State University, Raleigh, NC 27695-7906. hcheng01@yahoo.com;Industrial Engineering and Operations Research, North Carolina State University, Raleigh, NC 27695-7906. fang@eos.ncsu.edu;Mathematics Division, Army Research Office, Army Research Laboratory, P.O. Box 12211, Research Triangle Park, NC 27709-2211. john.lavery2@us.army.mil
Venue:
Computational Optimization and Applications
Year:
2004

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Abstract

An active set based algorithm for calculating the coefficients of univariate cubic L1 splines is developed. It decomposes the original problem in a geometric-programming setting into independent optimization problems of smaller sizes. This algorithm requires only simple algebraic operations to obtain an exact optimal solution in a finite number of iterations. In stability and computational efficiency, the algorithm outperforms a currently widely used discretization-based primal affine algorithm.