A Geometric Programming Framework for Univariate Cubic L 1 Smoothing Splines

Hao Cheng (), Shu-Cherng Fang () and John Lavery ()

Annals of Operations Research, 2005, vol. 133, issue 1, 229-248

Abstract: Univariate cubic L 1 smoothing splines are capable of providing shape-preserving C 1 -smooth approximation of multi-scale data. The minimization principle for univariate cubic L 1 smoothing splines results in a nondifferentiable convex optimization problem that, for theoretical treatment and algorithm design, can be formulated as a generalized geometric program. In this framework, a geometric dual with a linear objective function over a convex feasible domain is derived, and a linear system for dual to primal conversion is established. Numerical examples are given to illustrate this approach. Sensitivity analysis for data with uncertainty is presented. Copyright Springer Science + Business Media, Inc. 2005

Keywords: smoothing spline; geometric programming; data fitting; shape preservation; sensitivity analysis (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/s10479-004-5035-9

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