A geometric programming framework for univariate cubic L1 smoothing splines

A geometric programming framework for univariate cubic L1 smoothing splines

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Article ID: iaor20052325
Country: Netherlands
Volume: 133
Issue: 1
Start Page Number: 229
End Page Number: 248
Publication Date: Jan 2005
Journal: Annals of Operations Research
Authors: , ,
Abstract:

Univariate cubic L1 smoothing splines are capable of providing shape-preserving C1-smooth approximation of multi-scale data. The minimization principle for univariate cubic L1 smoothing splines results in a nondifferential 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.

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