Learning sub-patterns in piecewise continuous functions

Fitting piecewise linear continuous functions

We consider the problem of fitting a continuous piecewise linear function to a finite set of data points, modeled as a mathematical program with convex objective. We review some fitting problems that can be modeled as convex programs, and then introduce mixed-binary generalizations that allow variability in the regions defining the best-fit function’s domain. We also study the additional constr...

Continuity of super- and sub-additive transformations of continuous functions

We prove a continuity inheritance property for super- and sub-additive transformations of non-negative continuous multivariate functions defined on the domain of all non-negative points and vanishing at the origin. As a corollary of this result we obtain that super- and sub-additive transformations of continuous aggregation functions are again continuous aggregation functions.

Convex Underestimation of C2 Continuous Functions by Piecewise Quadratic Perturbation

Clifford A. Meyer and Christodoulos A. Floudas Department of Chemical Engineering, Princeton University, Princeton, NJ 08544, USA Abstract This paper presents an efficient branch and bound approach to address the global optimization of constrained optimization problems with twice differentiable functions. A lower bound on the global minimum is determined via a convex nonlinear programming probl...

A Modified Adaptive Quadrature Scheme for Continuous Piecewise-Smooth Functions

Irredundant lattice representations of continuous piecewise affine functions

In this paper, we revisit the lattice representation of continuous piecewise affine (PWA) function and give a formal proof of its representation ability. Based on this, we derive the irredundant lattice PWA representation through removal of redundant terms and literals. Necessary and sufficient conditions for irredundancy are proposed. Besides, we explain how to remove terms and literals in ord...