6533b855fe1ef96bd12b1117

RESEARCH PRODUCT

Solution isolation strategies for the Bernstein polytopes-based solver

Hichem BarkiMahfoud DjedainiDominique MichelucciSebti Foufou

subject

Constraint (information theory)Nonlinear systemMonomialMathematical optimizationLinear programmingComputer scienceBenchmark (computing)PolytopeSolverGeometric modeling

description

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.

yearjournalcountryeditionlanguage
2013-11-012013 7th IEEE GCC Conference and Exhibition (GCC)
https://doi.org/10.1109/ieeegcc.2013.6705782