Laminar M-Convex Minimization

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 the following M-convex functions for laminar:

• quadratic laminar M-convex function:
• quartic laminar M-convex function:
• exponential laminar M-convex function:
• logarithmic laminar M-convex function:

---

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.