{"ID":2863638,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.24829","arxiv_id":"2509.24829","title":"Continuous differentiability of the signum function and Newton's method for bang-bang control","abstract":"We investigate bang-bang control problems and the possibility to apply Newton's method to solve such kind of problems numerically. To this end, we show that the signum function is Fréchet differentiable between appropriate function spaces. Numerical experiments show the applicability of the resulting method.","short_abstract":"We investigate bang-bang control problems and the possibility to apply Newton's method to solve such kind of problems numerically. To this end, we show that the signum function is Fréchet differentiable between appropriate function spaces. Numerical experiments show the applicability of the resulting method.","url_abs":"https://arxiv.org/abs/2509.24829","url_pdf":"https://arxiv.org/pdf/2509.24829v1","authors":"[\"Daniel Wachsmuth\",\"Gerd Wachsmuth\"]","published":"2025-09-29T14:15:22Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}