A Shape-Newton Approach to the Problem of Covering with Identical Balls
| Autor: | Ernesto G. Birgin, Antoine Laurain, Rafael Massambone, Arthur G. Santana |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP |
| ISSN: | 1095-7197 1064-8275 |
| DOI: | 10.1137/21m1426067 |
| Popis: | The problem of covering a region of the plane with a fixed number of minimum-radius identical balls is studied in the present work. An explicit construction of bi-Lipschitz mappings is provided to model small perturbations of the union of balls. This allows us to obtain analytical expressions for first- and second-order derivatives using nonsmooth shape optimization techniques under appropriate regularity assumptions. Singular cases are also studied using asymptotic analysis. For the case of regions given by the union of disjoint convex polygons, algorithms based on Voronoi diagrams that do not rely on approximations are given to compute the derivatives. Extensive numerical experiments illustrate the capabilities and limitations of the introduced approach. |
| Databáze: | OpenAIRE |
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