3 papers
math.OC2022
Strong Stationarity Conditions for Optimal Control Problems Governed by a Rate-Independent Evolution Variational Inequality
Martin Brokate, Constantin Christof
We prove strong stationarity conditions for optimal control problems that are governed by a prototypical rate-independent evolution variational inequality, i.e., first-order necess…
math.AP2019
Weak differentiability of the control-to-state mapping in a parabolic equation with hysteresis
Martin Brokate, Klemens Fellner, Matthias Lang-Batsching
We consider the heat equation on a bounded domain subject to an inhomogeneous forcing in terms of a rate-independent (hysteresis) operator and a control variable. The aim of the pa…
math.FA2016
Newton and Bouligand derivatives of the scalar play and stop operator
Martin Brokate
We prove that the play and the stop operator possess Newton and Bouligand derivatives, and exhibit formulas for those derivatives. The remainder estimate is given in a strenghtened…