### 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) |
---|---|

Pages (from-to) | 55-63 |

Number of pages | 9 |

Journal | Journal of Optimization Theory and Applications |

Volume | 98 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1998 |

### Fingerprint

### 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

### Cite this

*Journal of Optimization Theory and Applications*,

*98*(1), 55-63. https://doi.org/10.1023/A:1022632713397

**Nearness and bound relationships between an integer-programming problem and its relaxed linear-programming problem.** / Joseph, Anito; Gass, S. I.; Bryson, N. A.

Research output: Contribution to journal › Article

*Journal of Optimization Theory and Applications*, vol. 98, no. 1, pp. 55-63. https://doi.org/10.1023/A:1022632713397

}

TY - JOUR

T1 - Nearness and bound relationships between an integer-programming problem and its relaxed linear-programming problem

AU - Joseph, Anito

AU - Gass, S. I.

AU - Bryson, N. A.

PY - 1998/1/1

Y1 - 1998/1/1

N2 - 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.

AB - 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.

KW - Extreme points

KW - Integer programming

KW - Relaxed linear-programming problems

KW - Solution bounds

UR - http://www.scopus.com/inward/record.url?scp=0032387057&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032387057&partnerID=8YFLogxK

U2 - 10.1023/A:1022632713397

DO - 10.1023/A:1022632713397

M3 - Article

AN - SCOPUS:0032387057

VL - 98

SP - 55

EP - 63

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

SN - 0022-3239

IS - 1

ER -