Related papers: Bouligand Analysis and Discrete Optimal Control of…
We investigate optimality conditions for optimization problems constrained by a class of variational inequalities of the second kind. Based on a nonsmooth primal-dual reformulation of the governing inequality, the differentiability of the…
We consider optimal control problems for a wide class of bilateral obstacle problems where the control appears in a possibly nonlinear source term. The non-differentiability of the solution operator poses the main challenge for the…
This paper is concerned with an optimal control problem governed by nonsmooth semilinear elliptic partial differential equations with both distributed and boundary unilateral pointwise control constraints, in which the nonlinear coefficient…
We investigate local optimality conditions of first and second order for integer optimal control problems with total variation regularization via a finite-dimensional switching point problem. We show the equivalence of local optimality for…
This paper is concerned with an optimal control problem governed by a non-smooth semilinear elliptic equation. We show that the control-to-state mapping is directionally differentiable and precisely characterize its Bouligand…
We prove that solution operators of elliptic obstacle-type variational inequalities (or, more generally, locally Lipschitz continuous functions possessing certain pointwise-a.e. convexity properties) are Newton differentiable when…
We focus on elliptic quasi-variational inequalities (QVIs) of obstacle type and prove a number of results on the existence of solutions, directional differentiability and optimal control of such QVIs. We give three existence theorems based…
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of…
We address the problem of optimal scale-dependent parameter learning in total variation image denoising. Such problems are formulated as bilevel optimization instances with total variation denoising problems as lower-level constraints. For…
We consider optimal control problems, where the control appears in the main part of the operator. We derive the Pontryagin maximum principle as a necessary optimality condition. The proof uses the concept of topological derivatives. In…
Quasi-variational inequalities (QVIs) of obstacle type in many cases have multiple solutions that can be ordered. We study a multitude of properties of the operator mapping the source term to the minimal or maximal solution of such QVIs. We…
We consider optimal control of an elliptic two-point boundary value problem governed by functions of bounded variation (BV). The cost functional is composed of a tracking term for the state and the BV-seminorm of the control. We use the…
This paper focuses on the analysis of an optimal control problem governed by a nonsmooth quasilinear partial differential equation that models a stationary incompressible shear-thickening fluid. We start by studying the directional…
We prove strong stationarity conditions for optimal control problems that are governed by a prototypical rate-independent evolution variational inequality, i.e., first-order necessary optimality conditions in the form of a primal-dual…
Variational inequalities are an important mathematical tool for modelling free boundary problems that arise in different application areas. Due to the intricate nonsmooth structure of the resulting models, their analysis and optimization is…
We reconsider the variational integration of optimal control problems for mechanical systems based on a direct discretization of the Lagrange-d'Alembert principle. This approach yields discrete dynamical constraints which by construction…
We propose a nonsmooth trust-region method for solving optimization problems with locally Lipschitz continuous functions, with application to problems constrained by variational inequalities of the second kind. Under suitable assumptions on…
We analyze optimal control problems for two-phase Navier-Stokes equations with surface tension. Based on $L_p$-maximal regularity of the underlying linear problem and recent well-posedness results of the problem for sufficiently small data…
Total variation integer optimal control problems admit solutions and necessary optimality conditions via geometric variational analysis. In spite of the existence of said solutions, algorithms which solve the discretized objective suffer…
This paper deals with generalized differentiability and second-order necessary optimality conditions for a box-constrained optimal control problem governed by an exponential semilinear elliptic equation with discrete measures as sources,…