### Abstract

This paper investigates the properties of the inclusion functions on subintervals while a Branch-and-Bound algorithm is solving global optimization problems. It has been found that the relative place of the global minimum value within the inclusion interval of the inclusion function of the objective function at the actual interval mostly indicates whether the given interval is close to a minimizer point. This information is used in a heuristic interval rejection rule that can save a big amount of computation. Illustrative examples are discussed and a numerical study completes the investigation.

Original language | English |
---|---|

Pages (from-to) | 683-692 |

Number of pages | 10 |

Journal | BIT Numerical Mathematics |

Volume | 41 |

Issue number | 4 |

Publication status | Published - Dec 2001 |

### Fingerprint

### Keywords

- Branch-and-bound algorithm
- Global optimization
- Inclusion function

### ASJC Scopus subject areas

- Computer Graphics and Computer-Aided Design
- Software
- Applied Mathematics
- Computational Mathematics

### Cite this

*BIT Numerical Mathematics*,

*41*(4), 683-692.

**A heuristic rejection criterion in interval global optimization algorithms.** / Casado, L. G.; García, I.; Csendes, T.

Research output: Contribution to journal › Article

*BIT Numerical Mathematics*, vol. 41, no. 4, pp. 683-692.

}

TY - JOUR

T1 - A heuristic rejection criterion in interval global optimization algorithms

AU - Casado, L. G.

AU - García, I.

AU - Csendes, T.

PY - 2001/12

Y1 - 2001/12

N2 - This paper investigates the properties of the inclusion functions on subintervals while a Branch-and-Bound algorithm is solving global optimization problems. It has been found that the relative place of the global minimum value within the inclusion interval of the inclusion function of the objective function at the actual interval mostly indicates whether the given interval is close to a minimizer point. This information is used in a heuristic interval rejection rule that can save a big amount of computation. Illustrative examples are discussed and a numerical study completes the investigation.

AB - This paper investigates the properties of the inclusion functions on subintervals while a Branch-and-Bound algorithm is solving global optimization problems. It has been found that the relative place of the global minimum value within the inclusion interval of the inclusion function of the objective function at the actual interval mostly indicates whether the given interval is close to a minimizer point. This information is used in a heuristic interval rejection rule that can save a big amount of computation. Illustrative examples are discussed and a numerical study completes the investigation.

KW - Branch-and-bound algorithm

KW - Global optimization

KW - Inclusion function

UR - http://www.scopus.com/inward/record.url?scp=0042318562&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042318562&partnerID=8YFLogxK

M3 - Article

VL - 41

SP - 683

EP - 692

JO - BIT Numerical Mathematics

JF - BIT Numerical Mathematics

SN - 0006-3835

IS - 4

ER -