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Classical cuts for mixed-integer programming and branch-and-cut.

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Title: Classical cuts for mixed-integer programming and branch-and-cut.
Authors: Padberg, Manfred
Source: Mathematical Methods of Operations Research. 2001, Vol. 53 Issue 2, p173. 31p.
Subjects: Integer programming, Cutting stock problem, Rings of integers
Abstract: We review classical valid linear inequalities for mixed-integer programming, i.e., Gomory's fractional and mixed-integer cuts, and discuss their use in branch-and-cut. In particular, a generalization of the recent mixed-integer rounding (MIR) inequality and a sufficient condition for the global validity of classical cuts after branching has occurred are derived. [ABSTRACT FROM AUTHOR]
Copyright of Mathematical Methods of Operations Research is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: We review classical valid linear inequalities for mixed-integer programming, i.e., Gomory's fractional and mixed-integer cuts, and discuss their use in branch-and-cut. In particular, a generalization of the recent mixed-integer rounding (MIR) inequality and a sufficient condition for the global validity of classical cuts after branching has occurred are derived. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Mathematical Methods of Operations Research is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        PageCount: 31
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      – SubjectFull: Integer programming
        Type: general
      – SubjectFull: Cutting stock problem
        Type: general
      – SubjectFull: Rings of integers
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