Quadratic M-Convex Minimization

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.

dimension n = 1 2 3 4 5 6 7

You can input parameters a_ij and b_i in the ranges 0 < a_ij≤ 50 and -50 ≤ b_i≤ 50. If the input does not satisfy the condition , 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.)

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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.

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Nobuyuki Tsuchimura, Satoko Moriguchi