Finding magic squares with the Douglas-Rachford algorithm
Optimization and Control
2019-02-25 v1
Abstract
In this expository paper, we show how to use the Douglas-Rachford algorithm as a successful heuristic for finding magic squares. The Douglas-Rachford algorithm is an iterative projection method for solving feasibility problems. Although its convergence is only guaranteed in the convex setting, the algorithm has been successfully applied to a number of similar nonconvex problems, such as solving Sudoku puzzles. We present two formulations of the nonconvex feasibility problem of finding magic squares, which are inspired by those of Sudoku, and test the Douglas-Rachford algorithm on them.
Keywords
Cite
@article{arxiv.1902.08478,
title = {Finding magic squares with the Douglas-Rachford algorithm},
author = {Francisco J. Aragón Artacho and Paula Segura Martínez},
journal= {arXiv preprint arXiv:1902.08478},
year = {2019}
}
Comments
22 pages, 12 figures