Pseudo-Separable Quartic L-Convex Minimization

For a finite set V={1,2,...,n} and a family of univariate discrete convex functions and indexed by and , the function defined by

is an L-convex function [1,2].

Here we consider a quartic L-convex function:

In this web application, you can choose the dimension n from 1 to 10.

dimension n = 1 2 3 4 5 6 7 8 9 10

You can input parameters s_ij, t_ij, a_i and b_i in the ranges 0 < s_ij, a_i<50 and -10< t_ij, b_i< 10.

You can also input an initial solution x.

s	1	2	3
1
2
3

t	1	2	3
1
2
3

	1	2	3
a
b
x

(Note: "Reset" button resets your inputs to default values.
An inappropriate input value will be replaced with a random number.)

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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