Related papers: Numerical approximation of regularized non-convex …
In this work, an adaptive edge element method is developed for an H(curl)-elliptic constrained optimal control problem. We use the lowest-order Nedelec's edge elements of first family and the piecewise (element-wise) constant functions to…
We propose in this paper a multilevel correction method to solve optimal control problems constrained by elliptic equations with the finite element method. In this scheme, solving optimization problem on the finest finite element space is…
This paper analyzes an interface-unfitted numerical method for distributed optimal control problems governed by elliptic interface equations. We follow the variational discretization concept to discretize the optimal control problems, and…
We discretize a risk-neutral optimal control problem governed by a linear elliptic partial differential equation with random inputs using a Monte Carlo sample-based approximation and a finite element discretization, yielding finite…
We consider a pointwise tracking optimal control problem for a semilinear elliptic partial differential equation. We derive the existence of optimal solutions and analyze first and, necessary and sufficient, second order optimality…
This paper analyzes two eXtended finite element methods (XFEMs) for linear quadratic optimal control problems governed by Poisson equation in non-convex domains. We follow the variational discretization concept to discretize the continuous…
We analyze space-time finite element methods for the numerical solution of distributed parabolic optimal control problems with energy regularization in the Bochner space $L^2(0,T;H^{-1}(\Omega))$. By duality, the related norm can be…
This paper presents a general convergence theory of penalty based numerical methods for elliptic constrained inequality problems, including variational inequalities, hemivariational inequalities, and variational-hemivariational…
In this paper, we discuss the numerical approximation of a distributed optimal control problem governed by the von Karman equations, defined in polygonal domains with point-wise control constraints. Conforming finite elements are employed…
We use uniform $W^{2,p}$ estimates to obtain corrector results for periodic homogenization problems of the form $A(x/\varepsilon):D^2 u_{\varepsilon} = f$ subject to a homogeneous Dirichlet boundary condition. We propose and rigorously…
We consider some boundary value tracking optimal control problem constrained by a Neumann boundary value problem for some elliptic partial differential equation where the control acts as right-hand side. This optimal control problem can be…
This paper introduces a new variational formulation for Dirichlet boundary control problem of elliptic partial differential equations, based on observations that the state and adjoint state are related through the control on the boundary of…
This article investigates the numerical approximation of shape optimization problems with PDE constraint on classes of convex domains. The convexity constraint provides a compactness property which implies well posedness of the problem.…
We provide a framework for the numerical approximation of distributed optimal control problems, based on least-squares finite element methods. Our proposed method simultaneously solves the state and adjoint equations and is $\inf$--$\sup$…
We consider an optimal control problem governed by a rate-inde\-pendent system with non-convex energy. The state equation is approximated by means of viscous regularization w.r.t.\ to hierarchy of two different Hilbert spaces. The…
We construct an efficient numerical scheme for solving obstacle problems in divergence form. The numerical method is based on a reformulation of the obstacle in terms of an L1-like penalty on the variational problem. The reformulation is an…
We construct and analyze a multiscale finite element method for an elliptic distributed optimal control problem with pointwise control constraints, where the state equation has rough coefficients. We show that the performance of the…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
This work is concerned with quasi-optimal a-priori finite element error estimates for the obstacle problem in the $L^2$-norm. The discrete approximations are introduced as solutions to a finite element discretization of an accordingly…
We consider a class of constrained optimization problems with a possibly nonconvex non-Lipschitz objective and a convex feasible set being the intersection of a polyhedron and a possibly degenerate ellipsoid. Such problems have a wide range…