DCP HOME

Quadratic M-Convex Minimization

For a symmetric matrix quadM-A with quadM-aij

for some quadM-w1wn, the associated quadratic form quadform is an M-convex function [1,2]. For n=4, such a matrix looks like
quadM-defA

Here we consider a quadratic M-convex function:
objfunc-quadM.

In this web application, you can choose the dimension n from 1 to 7.

dimension n =

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 quadM-w1wn, the unsatisfactory condition turns red.

You can also input an initial solution x.


A 1 2 3
1
2
3

1 2 3
b
x

(Note: "Reset" button resets your inputs to default values.)


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