In the present work, we apply a variational discretization proposed by the first author in [14] to Lavrentiev-regularized state constrained elliptic control problems. We extend the results of [18] and prove weak convergence of the adjoint states and multipliers of the regularized problems to their counterparts of the original problem. Further, we prove error estimates for finite element discret...

In this paper, we propose a continuation method for box constrained variational inequality problems. The continuation method is based on the class of Gabriel-Mor e smooth functions and has the following attractive features: It can start from any point; It has a simple and natural neighborhood deenition; It solves only one approximate Newton equation at each iteration; It converges globally line...

In this paper, we address density properties of intersections of convex sets in several function spaces. Using the concept of Γ-convergence, it is shown in a general framework, how these density issues naturally arise from the regularization, discretization or dualization of constrained optimization problems and from perturbed variational inequalities. A variety of density results (and countere...

We consider a simply constrained optimization reformulation of the KarushKuhn-Tucker conditions arising from variational inequalities. Based on this reformulation, we present a new Newton-type method for the solution of variational inequalities. The main properties of this method are: (a) it is well-defined for an arbitrary variational inequality problem, (b) it is globally convergent at least ...

We consider control-constrained linear-quadratic optimal control problems on evolving hypersurfaces in R. In order to formulate well-posed problems, we prove existence and uniqueness of weak solutions for the state equation, in the sense of vector-valued distributions. We then carry out and prove convergence of the variational discretization of a distributed optimal control problem. In the proc...