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Hausdorff distance between convex semialgebraic sets

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Abstract

In this paper, we proposed an approach for computing the Hausdorff distance between convex semialgebraic sets. We exploit the KKT conditions to rewrite the Hausdorff distance as polynomial maximization problems under some assumptions, in which polynomial and rational expressions of Lagrange multipliers are used. Then, polynomial maximization problems are solved by Lasserre’s hierarchy of semi-definite relaxations. Finally, some numerical examples are reported.

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Acknowledgements

The authors would like to thank the editors and anonymous referees for the valuable advice. Guangming Zhou was supported by Natural Science Foundation of China (12071399) and Key Projects of Hunan Provincial Education Department (18A048). Wenjie Zhao was supported by Postgraduate Scientific Research Innovation Project of Hunan Province (CX20210605).

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Authors and Affiliations

  1. School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, Hunan, China

    Wenjie Zhao

  2. Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, Hunan, China

    Guangming Zhou

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  1. Wenjie Zhao
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Correspondence to Guangming Zhou.

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Zhao, W., Zhou, G. Hausdorff distance between convex semialgebraic sets. J Glob Optim 88, 409–429 (2024). https://doi.org/10.1007/s10898-023-01313-9

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  • DOI: https://doi.org/10.1007/s10898-023-01313-9

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