M-Convex Functions on Jump Systems: A General Framework for Minsquare Graph Factor Problem

The METR technical reports are published as a means to ensure timely dissemination of scholarly and technical work on a non-commercial basis. Copyright and all rights therein are maintained by the authors or by other copyright holders, notwithstanding that they have offered their works here electronically. It is understood that all persons copying this information will adhere to the terms and constraints invoked by each author's copyright. These works may not be reposted without the explicit permission of the copyright holder. Abstract The concept of M-convex functions is generalized for functions defined on constant-parity jump systems. Such function arises from minimum weight perfect b-matchings and from a separable convex function (sum of univariate convex functions) on the degree sequences of an undirected graph. As a generalization of a recent result of Apollonio and Seb˝ o for the minsquare factor problem, a local optimality criterion is given for minimization of an M-convex function subject to a component sum constraint.