Routines for solving the overdetermined box-constrained integer least squares problem
$$
\min_{\boldsymbol{x}\in \mathbb{Z}^n,\ \boldsymbol{l} \leq \boldsymbol{x}\leq \boldsymbol{u}}\|\boldsymbol{y}-\boldsymbol{B}\boldsymbol{x}\|_2,
$$
where \(\boldsymbol{B}\) is a real matrix with full column rank, y is a real vector, and \(\boldsymbol{l}\) and \(\boldsymbol{u}\) are integer vectors
(note: entries of \(\boldsymbol{l}\) can be \(-\infty\) and entries of \(\boldsymbol{u}\) can be \(\infty\)) (last updated: December 2022):
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obils.m for a user who wants to view the source code.
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obils.zip (includes three files) for a user who wants to run the code faster (sub-functions are in MEX form)
Contributors: Xiao-Wen Chang, Xiangyu Ren, Jiequn Shen, Zhongjie Wu
If you use this package in your research work to be published, please include explicit mention of the package
in your publication:
X.-W. Chang. MILES: MATLAB package for solving mixed integer least squares problems,
School of Computer Science, McGill University, http://www.cs.mcgill.ca/~chang/software/MILES.php.
Last updated: December 2022.
The routines use the algorithms proposed in the following papers:
[1] S. Breen and X.-W. Chang.
Column Reordering for Box-constrained Integer Least Squares Problems,
Proceedings of IEEE GLOBECOM 2011, 6 pages.
[2] X.-W. Chang and Q. Han.
Solving Box-Constrained Integer Least Squares Problems,
IEEE Transactions on Wireless Communications, 7 (2008), pp. 277-287.