A Geometric Programming Framework for Univariate Cubic L 1 Smoothing Splines
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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.
Keywordssmoothing spline geometric programming data fitting shape preservation sensitivity analysis
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