A laminar family means a nonempty family of subsets of {1, ... , n} such that For a laminar family and a family of univariate discrete convex functions indexed by , the function defined by is an M-convex function [1,2], where Here we consider an exponential laminar M-convex function: for a laminar. In this web application, the laminar family is preset for each dimension. For example, = {{1},{2},{3}, {1,2}, {1,2,3}} in the 3-dimensional case. You can choose the dimension n from 1 to 9.
This web application minimizes f(x) using ODICON.
[1] K. Murota (2001): "Discrete Convex Analysis---An Introduction (in Japanese)," Kyoritsu Publishing Company, Tokyo. Section 4.3.
[2] K. Murota (2003): "Discrete Convex Analysis," SIAM. Section 6.3.
Satoko Moriguchi, Nobuyuki Tsuchimura