A Branch-and-Bound Approach for Estimating Covering Functionals of Convex Bodies

Chan He (), Yafang Lv (), Horst Martini () and Senlin Wu ()
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Chan He: North University of China
Yafang Lv: North University of China
Horst Martini: Technische Universität Chemnitz
Senlin Wu: North University of China

Journal of Optimization Theory and Applications, 2023, vol. 196, issue 3, No 10, 1036-1055

Abstract: Abstract Estimating covering functionals of convex bodies is not only interesting for its own, but also an important part of Chuanming Zong’s program to attack Hadwiger’s covering conjecture, a long-standing open problem from Discrete and Combinatorial Geometry. In general, it is difficult to determine exact values of the covering functionals of a convex body by theoretical analysis. Therefore we propose a global optimization algorithm based on the geometric branch-and-bound method. Numerical experiments have been carried out to estimate covering functionals of the Euclidean unit disc.

Keywords: Branch-and-bound; Convex body; Covering functional; Hadwiger’s covering problem; 52C17; 52A37 (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-022-02146-4

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