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Rigorous verification of feasibility

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Abstract

This paper considers the problem of finding and verifying feasible points for constraint satisfaction problems (CSPs), including those with uncertain coefficients. The main part is devoted to the problem of finding a narrow box around an approximately feasible solution for which it can be rigorously and automatically proved that it contains a feasible solution. Some examples demonstrate difficulties when attempting verification. We review some existing methods and present a new method for verifying the existence of feasible points of CSPs in an automatically determined narrow box. Numerical tests within GloptLab, a solver developed by the authors, show how the different methods perform. Also discussed are the search for approximately feasible points and the use of approximately feasible points within a branch and bound scheme for constraint satisfaction.

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Acknowledgments

This research was supported through the research grant P23554-N13 of the FWF (Fonds zur Förderung der wissenschaftlichen Forschung). We thank Baker Kearfott for answering our questions regarding his verification methods. We also thank the reviewer for the constructive suggestions.

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  1. Faculty of Mathematics, University of Vienna, Vienna, Austria

    Ferenc Domes & Arnold Neumaier

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  1. Ferenc Domes
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  2. Arnold Neumaier
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Correspondence to Ferenc Domes.

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Domes, F., Neumaier, A. Rigorous verification of feasibility. J Glob Optim 61, 255–278 (2015). https://doi.org/10.1007/s10898-014-0158-2

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