Xiao-Wen
CHANG
Teaching
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Software
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MILES: MATLAB package for solving Mixed Integer LEast Squares problems, 2006-2022.
Last updated: December 2022.
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.
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Routines for solving the standard integer least squares problem
$$
\min_{\boldsymbol{x} \in \mathbb{Z}^n}\|\boldsymbol{y}-\boldsymbol{B}\boldsymbol{x}\|_2,
$$
where \(\boldsymbol{B}\) is a real matrix with full column rank,
and \(\boldsymbol{y}\) is a real vector. December 2022.
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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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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, \(\boldsymbol{y}\) 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 \(\infty\)). December 2022.
-
Routines for solving the underdetermined 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 \(m \times n\) matrix with \(rank(\boldsymbol{B}) < n\), \(\boldsymbol{y}\) is a real vector, and \(\boldsymbol{l}\) and \(\boldsymbol{u}\) are finite integer vectors. December 2022.
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