Optimal Control and Directional Differentiability for Elliptic Quasi-Variational Inequalities

Abstract We focus on elliptic quasi-variational inequalities (QVIs) of obstacle type and prove a number results the existence solutions, directional differentiability optimal control such QVIs. give three theorems based an order approach, iteration scheme sequential regularisation through partial differential equations. show that solution map taking source term into set solutions QVI is directionally differentiable for general data locally Hadamard mappings, thereby extending in particular our previous work which provided first result QVIs infinite dimensions. Optimal problems with constraints are also considered we derive various forms stationarity conditions problems, thus supplying among this area.