Mathematical programming formulations for piecewise polynomial functions

Locally ideal formulations for piecewise linear functions with indicator variables

In this paper, we consider mixed integer linear programming (MIP) formulations for piecewise linear functions (PLFs) that are evaluated when an indicator variable is turned on. We describe modifications to standard MIP formulations for PLFs with desirable theoretical properties and superior computational performance in this context. © 2013 Elsevier B.V. All rights reserved.

Extending Piecewise Polynomial Functions in Two Variables

We study the extensibility of piecewise polynomial functions defined on closed subsets of R2 to all of R2. The compact subsets of R2 on which every piecewise polynomial function is extensible to R2 can be characterized in terms of local quasi-convexity if they are definable in an o-minimal expansion of R. Even the noncompact closed definable subsets can be characterized if semialgebraic functio...

Numerical Technique for the Convolution of Piecewise Polynomial Functions

Computing Contour Trees for 2D Piecewise Polynomial Functions

Contour trees are extensively used in scalar field analysis. The contour tree is a data structure that tracks the evolution of level set topology in a scalar field. Scalar fields are typically available as samples at vertices of a mesh and are linearly interpolated within each cell of the mesh. A more suitable way of representing scalar fields, especially when a smoother function needs to be mo...

Universal algorithms for learning theory Part II : piecewise polynomial functions

This paper is concerned with estimating the regression function fρ in supervised learning by utilizing piecewise polynomial approximations on adaptively generated partitions. The main point of interest is algorithms that with high probability are optimal in terms of the least square error achieved for a given number m of observed data. In a previous paper [1], we have developed for each β > 0 a...