Moriguchi, Satoko; Murota, Kazuo On fundamental operations for multimodular functions. (English) Zbl 1426.90081 J. Oper. Res. Soc. Japan 62, No. 2, 53-63 (2019). Summary: Multimodular functions, primarily used in the literature of queueing theory, discrete-event systems, and operations research, constitute a fundamental function class in discrete convex analysis. The objective of this paper is to clarify the properties of multimodular functions with respect to fundamental operations such as permutation and scaling of variables, projection (partial minimization) and convolution. It is shown, in particular, that the class of multimodular functions is stable under projection under a certain natural condition on the variables to be minimized, and the convolution of two multimodular functions is not necessarily multimodular, even in the special case of the convolution of a multimodular function with a separable convex function. Cited in 5 Documents MSC: 90B22 Queues and service in operations research 90C25 Convex programming Keywords:discrete optimization; discrete convex analysis; multimodular function; \(L\)-convex function; projection; infimal convolution PDFBibTeX XMLCite \textit{S. Moriguchi} and \textit{K. Murota}, J. Oper. Res. Soc. Japan 62, No. 2, 53--63 (2019; Zbl 1426.90081) Full Text: arXiv