Annals of Operations Research

, Volume 133, Issue 1–4, pp 229–248 | Cite as

A Geometric Programming Framework for Univariate Cubic L 1 Smoothing Splines

  • Hao Cheng
  • Shu-Cherng FangEmail author
  • John E. Lavery


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.


smoothing spline geometric programming data fitting shape preservation sensitivity analysis 


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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Industrial Engineering Department and Operations Research ProgramNorth Carolina State UniversityRaleighUSA
  2. 2.Mathematics DivisionArmy Research Office, Army Research LaboratoryResearch Triangle ParkUSA

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