### Abstract

We discuss relationships between the solution to an integer-programming problem and the solution to its relaxed linear-program-ming problem in terms of the distance that separates them and related bounds. Assuming knowledge of a subset of extreme points, we develop bounds for associated convex combinations and show how improved bounds on the integer-programming problem's objective function and variables can be obtained.

Original language | English (US) |
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Pages (from-to) | 55-63 |

Number of pages | 9 |

Journal | Journal of Optimization Theory and Applications |

Volume | 98 |

Issue number | 1 |

DOIs | |

State | Published - Jul 1998 |

### Keywords

- Extreme points
- Integer programming
- Relaxed linear-programming problems
- Solution bounds

### ASJC Scopus subject areas

- Control and Optimization
- Management Science and Operations Research
- Applied Mathematics

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## Cite this

Joseph, A., Gass, S. I., & Bryson, N. A. (1998). Nearness and bound relationships between an integer-programming problem and its relaxed linear-programming problem.

*Journal of Optimization Theory and Applications*,*98*(1), 55-63. https://doi.org/10.1023/A:1022632713397