Routines for solving the standard mixed integer least squares problem
$$
\min_{\boldsymbol{x} \in \mathbb{R}^k,\ \mathbb{z} \in \mathbb{Z}^n}\|\boldsymbol{y}-\boldsymbol{A}\boldsymbol{x}-\boldsymbol{B}\boldsymbol{z}\|_2,
$$
where \(\boldsymbol{A}\) and \(\boldsymbol{B}\) are real matrices, \([\boldsymbol{A},\boldsymbol{B}]\) has full column rank,
and \(\boldsymbol{y}\) is a real vector (December 2022):
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smils.m for a user who wants to view the source code.
-
smils.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, Zhongjie Wu, Xiaohu Xie, Tianyang Zhou
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] X.-W. Chang and T. Zhou.
MILES: MATLAB package for solving Mixed Integer
LEast Squares problems, GPS Solutions, 11 (2007), pp. 289-294.
[2] X. Xie, X.-W. Chang, and M. Al Borno.
Partial LLL reduction,
Proceedings of IEEE GLOBECOM 2011, 5 pages.
[3] X.-W. Chang, X. Yang, and T. Zhou.
MLAMBDA: A Modified LAMBDA Method
for Integer Least-squares Estimation, Journal of Geodesy, 79 (2005), pp. 552-565.
[4] A. Ghasemmehdi and E. Agrell. Faster Recursions in Sphere Decoding,
IEEE Transactions on Information Theory, 57 (2011), pp. 3530-3536