On basic operations related to network induction of discrete convex functions. (4th May 2021)

• Record Type: Journal Article
• Authors: Murota, Kazuo
• Is Part Of: Optimization methods and software. Volume 36:Number 2/3(2021)
• Page Start: 519
• Page End: 559
• Publication Date: 2021-05-04
• Subjects: Discrete convex analysis -- integrally convex function -- multimodular function -- splitting -- aggregation -- network induction; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2020.1818080
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : Discrete convex functions are used in many areas, including operations research, discrete-event systems, game theory, and economics. The objective of this paper is to investigate basic operations such as direct sum, splitting, and aggregation that are related to network induction of discrete convex functions as well as discrete convex sets. Various kinds of discrete convex functions in discrete convex analysis are considered such as integrally convex functions, L-convex functions, M-convex functions, multimodular functions, and discrete midpoint convex functions.