Interval-based projection method for under-constrained numerical systems

Daisuke Ishii, Alexandre Goldsztejn, Christophe Jermann

    Research output: Contribution to journalArticle

    18 Citations (Scopus)

    Abstract

    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
    JournalConstraints
    Volume17
    Issue number4
    DOIs
    Publication statusPublished - 2012 Oct

    Fingerprint

    Projection Method
    Projection
    Interval
    Solution Set
    Nonlinear Constraints
    Constrained Systems
    Equality Constraints
    Inequality Constraints
    Pruning
    Branching
    Branch
    Experimental Results

    Keywords

    • 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

    Cite this

    Interval-based projection method for under-constrained numerical systems. / Ishii, Daisuke; Goldsztejn, Alexandre; Jermann, Christophe.

    In: Constraints, Vol. 17, No. 4, 10.2012, p. 432-440.

    Research output: Contribution to journalArticle

    Ishii, Daisuke ; Goldsztejn, Alexandre ; Jermann, Christophe. / Interval-based projection method for under-constrained numerical systems. In: Constraints. 2012 ; Vol. 17, No. 4. pp. 432-440.
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