- Geometric Dual Formulation for First-derivative-based Univariate Cubic $L_1$ Splines Y.B. Zhao (ybzhaoamss.ac.cn) S.C. Fang (fangeos.ncsu.edu) J.E. Lavery (john.lavery2us.army.mil) Abstract: With the objective of generating shape-preserving'' smooth interpolating curves that represent data with abrupt changes in magnitude and/or knot spacing, we study a class of first-derivative-based ${\cal C}^1$-smooth univariate cubic $L_1$ splines. An $L_1$ spline minimizes the $L_1$ norm of the difference between the first-order derivative of the spline and the local divided difference of the data. Calculating the coefficients of an $L_1$ spline is a nonsmooth nonlinear convex program. Via Fenchel's conjugate transformation, the geometric dual program is a smooth convex program with a linear objective function and convex cubic constraints. The dual-to-primal transformation is accomplished by solving a linear program. Keywords: Conjugate function, convex program, cubic $L_1$ spline, shape-preserving interpolation Category 1: Applications -- Science and Engineering Category 2: Convex and Nonsmooth Optimization Category 3: Nonlinear Optimization Citation: Download: [PDF]Entry Submitted: 08/11/2006Entry Accepted: 08/12/2006Entry Last Modified: 08/11/2006Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society and by the Optimization Technology Center.