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arXiv · 2509.24829

Continuous differentiability of the signum function and Newton's method for bang-bang control

Daniel Wachsmuth·Gerd Wachsmuth
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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 Fr\'echet differentiable between appropriate function spaces. Numerical experiments show the applicability of the resulting method.

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Daniel Wachsmuth, Gerd Wachsmuth. 2025-09-29. Continuous differentiability of the signum function and Newton's method for bang-bang control. https://arxiv.org/abs/2509.24829

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