Interval-based projection method for under-constrained numerical systems

Daisuke Ishii*, Alexandre Goldsztejn, Christophe Jermann

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    20 Citations (Scopus)


    This paper presents an interval-based method that follows the branch-and-prune scheme to compute a verified paving of a projection of the solution set of an under-constrained system. Benefits of this algorithm include anytime solving process, homogeneous verification of inner boxes, and applicability to generic problems, allowing any number of (possibly nonlinear) equality and inequality constraints. We present three key improvements of the algorithm dedicated to projection problems: (i) The verification process is enhanced in order to prove faster larger boxes in the projection space. (ii) Computational effort is saved by pruning redundant portions of the solution set that would project identically. (iii) A dedicated branching strategy allows reducing the number of treated boxes. Experimental results indicate that various applications can be modeled as projection problems and can be solved efficiently by the proposed method.

    Original languageEnglish
    Pages (from-to)432-440
    Number of pages9
    Issue number4
    Publication statusPublished - 2012 Oct


    • Existentially quantified constraints
    • Interval analysis
    • Numerical constraint programming
    • Projection method
    • Under-constrained systems

    ASJC Scopus subject areas

    • Artificial Intelligence
    • Computational Theory and Mathematics
    • Software
    • Discrete Mathematics and Combinatorics


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