Quadratic L-Convex Minimization

For a symmetric matrix with the associated quadratic form is an L-convex function [1,2].

Here we consider a quadratic L-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 -5 ≤ a_ij≤ 0, 0 < a_ii≤ 50 and -100 ≤ b_i≤ 100. 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 5.2.

[2] K. Murota (2003): "Discrete Convex Analysis," SIAM. Section 7.3.

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Nobuyuki Tsuchimura, Satoko Moriguchi