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.
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This work is supported by research grant #DAAG55-98-D-0003 of the Army Research Office, USA.
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Cheng, H., Fang, SC. & Lavery, J.E. A Geometric Programming Framework for Univariate Cubic L 1 Smoothing Splines. Ann Oper Res 133, 229–248 (2005). https://doi.org/10.1007/s10479-004-5035-9
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DOI: https://doi.org/10.1007/s10479-004-5035-9