1 citations · 2 across the 7 of their papers we have counts for
7 papers
Second-order conditions for bang-bang control of elliptic equations in arbitrary dimensions
Gerd Wachsmuth
We consider an optimal control problem governed by a semilinear PDE in cases where the optimal control is of bang-bang type. By utilizing the theory of Bessel potential space, we c…
New numerical solutions to Newton's problem of least resistance via a convex hull approach
Gerd Wachsmuth
We present a numerical method for the solution of Newton's problem of least resistance in the class of convex functions using a convex hull approach. We observe that the numericall…
Continuous differentiability of the signum function and Newton's method for bang-bang control
Daniel Wachsmuth, Gerd Wachsmuth
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…
No-gap second-order optimality conditions for additive manufacturing
Hiba Hmede, Luc Paquet, Gerd Wachsmuth
Additive manufacturing by laser fusion on a metal oxides powder bed has developed considerably in the last few years and allows to produce a wide range of complex parts. The mathem…
A convex, finite and lower semicontinuous function with empty subdifferential
Gerd Wachsmuth
We give an example of a convex, finite and lower semicontinuous function whose subdifferential is everywhere empty. This is possible since the function is defined on an incomplete…
Numerical Approximation of Optimal Convex Shapes in
Sören Bartels, Hedwig Keller, Gerd Wachsmuth
In the optimization of convex domains under a PDE constraint numerical difficulties arise in the approximation of convex domains in . Previous research used a restric…
Hunting for reduced polytopes
Bernardo González Merino, Thomas Jahn, Gerd Wachsmuth
By correcting an example by Polyanskii, we show that there exist reduced polytopes in three-dimensional Euclidean space. This partially answers the question posed by Lassak on the…