A Geometric Programming Framework for Univariate Cubic L 1 Smoothing Splines |
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Authors: | Hao Cheng Shu-Cherng Fang John E. Lavery |
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Affiliation: | (1) Industrial Engineering Department and Operations Research Program, North Carolina State University, Raleigh, NC 27695-7906, USA;(2) Mathematics Division, Army Research Office, Army Research Laboratory, P.O. Box 12211, Research Triangle Park, NC 27709-2211, USA |
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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. This work is supported by research grant #DAAG55-98-D-0003 of the Army Research Office, USA. |
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Keywords: | smoothing spline geometric programming data fitting shape preservation sensitivity analysis |
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