A laminar family means a nonempty family of subsets of {1, ... , n} such thatFor 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.

Satoko Moriguchi(satoko(a)aiit.ac.jp) Replace '(a)' with '@' modified on 5/4 0:05, 2012 |