5 papers · 1 filter
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…