2021/08/09 by Nils Schlüter, Schlüter, Nils, Moritz Schulze Darup +1
Chemistry · Computer Science · Engineering · Mathematics · #Advanced Control Systems Optimization #Affine transformation #Chemistry #Computer science #Conic optimization #Convex analysis #Convex combination #Convex function #Convex optimization #Decomposition #Effective domain #Fault Detection and Control Systems #Function (biology) #Geometry #Machine Learning and Algorithms #Mathematical analysis #Mathematical optimization #Mathematics #Piecewise #Proper convex function #Pseudoconvex function #Pure mathematics #Regular polygon #Subderivative #cs.SY #eess.SY #math.OC
paper · pdf · doi:10.48550/arxiv.2108.03950
10 pages, 5 figures. Previously published at the 21st IFAC World Congress 2020
arxiv created 2021/08/09 · openalex publication_date 2021/08/09 · arxiv updated 2021/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we present a novel approach to decompose a given piecewise affine (PWA) function into two convex PWA functions. Convex decompositions are useful to speed up or distribute evaluations of PWA functions. Different approaches to construct a convex decomposition have already been published. However, either the two resulting convex functions have very high or very different complexities, which is often undesirable, or the decomposition procedure is inapplicable even for simple cases. Our novel methodology significantly reduces these drawbacks in order to extend the applicability of convex decompositions.