Study of the numerical efficiency of structured abs-normal forms. (3rd September 2021)

• Record Type: Journal Article
• Authors: Bosse, Torsten Falko; Narayanan, Sri Hari Krishna
• Is Part Of: Optimization methods and software. Volume 36:Number 5(2021)
• Page Start: 909
• Page End: 933
• Publication Date: 2021-09-03
• Subjects: Piecewise Linear Functions -- algorithmic Differentiation -- abs Normal Form -- structural Investigation; 65F99 -- 68W99 -- 65C20; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2019.1613654
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : The abs-normal form (ANF) can be used to represent almost any piecewise linear function. Several of these piecewise linear functions exhibit a certain structure that has an impact on the numerical efficiency of the ANF representation. In this paper, three common structures are investigated that typically arise in applications and require special numerical treatment: the sum, the composition, and the component-wise maximum/minimum of several functions. For these structures, the corresponding expressions of the resulting abs-normal form are provided, as well as some alternatives. The theoretical observations are supported by numerical results.