A geometric programming approach for bivariate cubic L1 splines

Bivariate cubic L1 splines provide C1-smooth, shape-preserving interpolation of arbitrary data, including data with abrupt changes in spacing and magnitude. The minimization principle for bivariate cubic L1 splines results in a nondifferentiable convex optimization problem. This problem is reformulated as a generalized geometric programming problem. A geometric dual with a linear objective function and convex cubic constraints is derived. A linear system for dual-to-primal conversion is established. The results of computational experiments are presented.