School of Computer Science

Xiao-Wen CHANG

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  • COMP 350
    Numerical Computing
  • COMP 540
    Matrix Computations
  • COMP 642
    Numerical Estimation
  • Software

    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.

    • 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.

    • 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.

    • 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.