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Interval-based projection method for under-constrained numerical systems

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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.

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Authors and Affiliations

  1. JSPS, National Institute of Informatics, Tokyo, Japan

    Daisuke Ishii

  2. CNRS, LINA (UMR 6241), Nantes, France

    Alexandre Goldsztejn

  3. University of Nantes, LINA (UMR 6241), Nantes, France

    Christophe Jermann

Authors
  1. Daisuke Ishii
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  2. Alexandre Goldsztejn
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  3. Christophe Jermann
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Correspondence to Daisuke Ishii.

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Ishii, D., Goldsztejn, A. & Jermann, C. Interval-based projection method for under-constrained numerical systems. Constraints 17, 432–460 (2012). https://doi.org/10.1007/s10601-012-9126-y

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  • DOI: https://doi.org/10.1007/s10601-012-9126-y

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