### Abstract

The Bernstein polytopes-based solver is a new method developed to solve systems of nonlinear equations, which often occur in Geometric Constraint Solving Problems. The principle of this solver is to linearize nonlinear monomials and then to solve the resulting linear programming problems, through linear programming. However, without any strategy for the isolation of the many solutions of multiple-solution systems, this solver is slow in practice. To overcome this problem, we propose in this work, a study of several strategies for solution isolation, through the split of solution boxes into several subboxes, according to three main steps answering the questions: when, where, and how to perform a split? We provide a detailed benchmark evaluating both time and space complexities for the proposed splitting strategies, applied to several Geometric Constraint Solving Problems widely encountered in geometric modeling. We also compare several linear programming solvers within our Bernstein solver.

Original language | English (US) |
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Title of host publication | 2013 7th IEEE GCC Conference and Exhibition, GCC 2013 |

Pages | 234-239 |

Number of pages | 6 |

DOIs | |

State | Published - Dec 1 2013 |

Event | 2013 7th IEEE GCC Conference and Exhibition, GCC 2013 - Doha, Qatar Duration: Nov 17 2013 → Nov 20 2013 |

### Other

Other | 2013 7th IEEE GCC Conference and Exhibition, GCC 2013 |
---|---|

Country | Qatar |

City | Doha |

Period | 11/17/13 → 11/20/13 |

### Fingerprint

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

*2013 7th IEEE GCC Conference and Exhibition, GCC 2013*(pp. 234-239). [6705782] https://doi.org/10.1109/IEEEGCC.2013.6705782

**Solution isolation strategies for the Bernstein polytopes-based solver.** / Djedaini, Mahfoud; Barki, Hichem; Foufou, Sebti; Michelucci, Dominique.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*2013 7th IEEE GCC Conference and Exhibition, GCC 2013.*, 6705782, pp. 234-239, 2013 7th IEEE GCC Conference and Exhibition, GCC 2013, Doha, Qatar, 11/17/13. https://doi.org/10.1109/IEEEGCC.2013.6705782

}

TY - GEN

T1 - Solution isolation strategies for the Bernstein polytopes-based solver

AU - Djedaini, Mahfoud

AU - Barki, Hichem

AU - Foufou, Sebti

AU - Michelucci, Dominique

PY - 2013/12/1

Y1 - 2013/12/1

N2 - The Bernstein polytopes-based solver is a new method developed to solve systems of nonlinear equations, which often occur in Geometric Constraint Solving Problems. The principle of this solver is to linearize nonlinear monomials and then to solve the resulting linear programming problems, through linear programming. However, without any strategy for the isolation of the many solutions of multiple-solution systems, this solver is slow in practice. To overcome this problem, we propose in this work, a study of several strategies for solution isolation, through the split of solution boxes into several subboxes, according to three main steps answering the questions: when, where, and how to perform a split? We provide a detailed benchmark evaluating both time and space complexities for the proposed splitting strategies, applied to several Geometric Constraint Solving Problems widely encountered in geometric modeling. We also compare several linear programming solvers within our Bernstein solver.

AB - The Bernstein polytopes-based solver is a new method developed to solve systems of nonlinear equations, which often occur in Geometric Constraint Solving Problems. The principle of this solver is to linearize nonlinear monomials and then to solve the resulting linear programming problems, through linear programming. However, without any strategy for the isolation of the many solutions of multiple-solution systems, this solver is slow in practice. To overcome this problem, we propose in this work, a study of several strategies for solution isolation, through the split of solution boxes into several subboxes, according to three main steps answering the questions: when, where, and how to perform a split? We provide a detailed benchmark evaluating both time and space complexities for the proposed splitting strategies, applied to several Geometric Constraint Solving Problems widely encountered in geometric modeling. We also compare several linear programming solvers within our Bernstein solver.

UR - http://www.scopus.com/inward/record.url?scp=84893621553&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84893621553&partnerID=8YFLogxK

U2 - 10.1109/IEEEGCC.2013.6705782

DO - 10.1109/IEEEGCC.2013.6705782

M3 - Conference contribution

AN - SCOPUS:84893621553

SN - 9781479907243

SP - 234

EP - 239

BT - 2013 7th IEEE GCC Conference and Exhibition, GCC 2013

ER -