joint work with Debdas Ghosh
In this paper, we study an inexact line search Newton method to solve a generalized Nash equilibrium problem (GNEP). The GNEP is an extension of classical Nash equilibrium problem, where feasible set depends on the strategies of the other players. In this paper, we have taken a particular class of GNEP in which the objective function and the constraint mappings are convex. The proposed method converges globally and also has a faster rate of convergence as compared to previous methods.
joint work with Michael Hintermüller, Carlos Rautenberg
We consider compliant obstacle problems, where two elastic membranes enclose a constant volume. The existence of solutions to this quasi-variational inequality (QVI)is established building on fixed-point arguments and partly on Mosco-convergence. Founded on the analytical findings, the solution of the QVI is approached by solving a sequence of variational inequalities (VIs). Each of these VIs is tackled in function space via a path-following semismooth Newton method. The numerical performance of the algorithm is enhanced by using adaptive finite elements based on a posteriori error estimation.
joint work with Sarvesh Kumar, Ricardo Ruiz-Baier
We introduce a discontinuous finite volume method for the approximation of distributed optimal control problems governed by the Brinkman equations, where a force field is sought such that it produces a desired velocity profile. The discretisation of state and co-state variables follows a lowest-order scheme, whereas three different approaches are used for the control representation: a variational discretisation and approximation through piecewise constant or piecewise linear elements. We employ the optimise-then-discretise approach, resulting in a non-symmetric discrete formulation. A priori error estimates for velocity, pressure, and control in natural norms are derived, and a set of numerical examples is presented to illustrate the performance of the method and to confirm the predicted accuracy of the generated approximations under various scenarios.