Hausdorff distance between convex semialgebraic sets

Wenjie Zhao () and Guangming Zhou ()
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Wenjie Zhao: Xiangtan University
Guangming Zhou: Xiangtan University

Journal of Global Optimization, 2024, vol. 88, issue 2, No 6, 409-429

Abstract: 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.

Keywords: Hausdorff distance; The KKT conditions; Expressions of Lagrange multipliers; Polynomial optimization; Lasserre’s hierarchy (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10898-023-01313-9

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