Solution isolation strategies for the Bernstein polytopes-based solver

Mahfoud Djedaini, Hichem Barki, Sebti Foufou, Dominique Michelucci

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish (US)
Title of host publication2013 7th IEEE GCC Conference and Exhibition, GCC 2013
Pages234-239
Number of pages6
DOIs
StatePublished - Dec 1 2013
Event2013 7th IEEE GCC Conference and Exhibition, GCC 2013 - Doha, Qatar
Duration: Nov 17 2013Nov 20 2013

Other

Other2013 7th IEEE GCC Conference and Exhibition, GCC 2013
CountryQatar
CityDoha
Period11/17/1311/20/13

Fingerprint

Linear programming
Nonlinear equations

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

Djedaini, M., Barki, H., Foufou, S., & Michelucci, D. (2013). Solution isolation strategies for the Bernstein polytopes-based solver. In 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.

2013 7th IEEE GCC Conference and Exhibition, GCC 2013. 2013. p. 234-239 6705782.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Djedaini, M, Barki, H, Foufou, S & Michelucci, D 2013, Solution isolation strategies for the Bernstein polytopes-based solver. in 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
Djedaini M, Barki H, Foufou S, Michelucci D. Solution isolation strategies for the Bernstein polytopes-based solver. In 2013 7th IEEE GCC Conference and Exhibition, GCC 2013. 2013. p. 234-239. 6705782 https://doi.org/10.1109/IEEEGCC.2013.6705782
Djedaini, Mahfoud ; Barki, Hichem ; Foufou, Sebti ; Michelucci, Dominique. / Solution isolation strategies for the Bernstein polytopes-based solver. 2013 7th IEEE GCC Conference and Exhibition, GCC 2013. 2013. pp. 234-239
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