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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…
No-gap second-order conditions for minimization problems in spaces of measures
Gerd Wachsmuth, Daniel Walter
Over the last years, minimization problems over spaces of measures have received increased interest due to their relevance in the context of inverse problems, optimal control and m…
Energy Space Newton Differentiability for Solution Maps of Unilateral and Bilateral Obstacle Problems
Constantin Christof, Gerd Wachsmuth
We prove that the solution operator of the classical unilateral obstacle problem on a nonempty open bounded set , , is Newton differentiabl…
Non-existence of perturbed solutions under a second-order sufficient condition
Gerd Wachsmuth
We present an optimization problem in infinite dimensions which satisfies the usual second-order sufficient condition but for which perturbed problems fail to possess solutions.