For a symmetric matrix with for some , the associated quadratic form is an M-convex function [1,2]. For n=4, such a matrix looks like
Here we consider a quadratic M-convex function:
. In this web application, you can choose the dimension n from 1 to 7. You can input parameters aij and bi in the ranges 0 < aij≤ 50 and -50 ≤ bi≤ 50. If the input does not satisfy the condition , the unsatisfactory condition turns red. You can also input an initial solution x.
This web application minimizes f(x) using ODICON.
[1] K. Murota (2001): "Discrete Convex Analysis---An Introduction (in Japanese)," Kyoritsu Publishing Company, Tokyo. Section 5.6.
[2] K. Murota (2003): "Discrete Convex Analysis," SIAM. Section 6.3.
Nobuyuki Tsuchimura, Satoko Moriguchi