Related papers: A note on functional a posteriori estimates for el…
In this two-part study we develop a general approach to the design and analysis of exact penalty functions for various optimal control problems, including problems with terminal and state constraints, problems involving differential…
We consider an optimal control problem governed by a one-dimensional elliptic equation that involves univariate functions of bounded variation as controls. For the discretization of the state equation we use linear finite elements and for…
We consider a linear-quadratic elliptic optimal control problem with point evaluations of the state variable in the cost functional. The state variable is discretized by conforming linear finite elements. For control discretization, three…
We consider an optimization problem related to elliptic PDEs of the form $-{\rm div}(a(x)\nabla u)=f$ with Dirichlet boundary condition on a given domain $\Omega$. The coefficient $a(x)$ has to be determined, in a suitable given class of…
Computational approaches to PDE-constrained optimization under uncertainty may involve finite-dimensional approximations of control and state spaces, sample average approximations of measures of risk and reliability, smooth approximations…
Optimal control problems for semilinear elliptic equations with control costs in the space of bounded variations are analysed. BV-based optimal controls favor piecewise constant, and hence 'simple' controls, with few jumps. Existence of…
In this article we develop function-based a posteriori error estimators for the solution of linear second order elliptic problems considering hierarchical spline spaces for the Galerkin discretization. We prove a global upper bound for the…
We consider an elliptic optimal control problem where the objective functional contains an integral along a surface of codimension 1, also known as a hypersurface. In particular, we use a fidelity term that encourages the state to take…
This paper gives an existence result for solutions to an elliptic optimal control problem based on a general fractional kernel, where the admissible controls come from a class satisfying both a growth bound and a superlinear-subcritical…
We provide an a priori analysis of collocation methods for solving elliptic boundary value problems. They begin with information in the form of point values of the data and utilize only this information to numerically approximate the…
We propose and analyze a reliable and efficient a posteriori error estimator for the pointwise tracking optimal control problem of the Stokes equations. This linear-quadratic optimal control problem entails the minimization of a cost…
The purpose of this work is the design and analysis of a reliable and efficient a posteriori error estimator for the so-called pointwise tracking optimal control problem. This linear-quadratic optimal control problem entails the…
We investigate optimal control problems governed by the elliptic partial differential equation $-\Delta u=f$ subject to Dirichlet boundary conditions on a given domain $\Omega$. The control variable in this setting is the right-hand side…
We propose and analyze a posteriori error estimates for a control-constrained optimal control problem with bang-bang solutions. We consider a solution strategy based on the variational approach, where the control variable is not…
The paper is concerned with guaranteed a posteriori error estimates for a class of evolutionary problems related to poroelastic media governed by the quasi-static linear Biot equations. The system is decoupled employing the fixed-stress…
We propose and analyze a reliable and efficient a posteriori error estimator for a constrained linear-quadratic optimal control problem involving Dirac measures; the control variable corresponds to the amplitude of forces modeled as point…
In the present work, we derive functional upper bounds for the potential error arising from finite-element boundary-element coupling formulations for a nonlinear Poisson-type transmission problem. The proposed a posteriori error estimates…
We consider an optimal control problem for the obstacle problem with an elliptic variational inequality. The obstacle function which is the control function is assumed in $H^{2}$. We use an approximate technique to introduce a family of…
This paper introduces a novel approach to the optimal control of linear discrete-time systems subject to bounded disturbances. Our approach is based on the newly established duality between ellipsoidal approximations of reachable and hardly…
In this paper we study an optimal control problem (OCP) associated to a linear elliptic equation {on a bounded domain $\Omega$}. The matrix-valued coefficients A of such systems is our control taken in L2 which in particular may comprise…