Authors: Hannes Meinlschmidt ; Christian Meyer ; Stephan Walther

The paper is concerned with an optimal control problem governed by a state equation in form of a generalized abstract operator differential equation involving a maximal monotone operator. The state equation is uniquely solvable, but the associated solution operator is in general not Gâteaux-differentiable. In order to derive optimality conditions, we therefore regularize the state equation and its solution operator, respectively, by means of a (smoothed) Yosida approximation. We show convergence of global minimizers for regularization parameter tending to zero and derive necessary and sufficient optimality conditions for the regularized problems. The paper ends with an application of the abstract theory to optimal control of homogenized quasi-static elastoplasticity.

• 49J40 - Variational inequalities
• 49K27 - Optimality conditions for problems in abstract spaces
• 74C05 - Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)