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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…

Optimization and Control · Mathematics 2017-10-26 Eduardo Casas , Karl Kunisch

Space-time finite element discretizations of time-optimal control problems governed by linear parabolic PDEs and subject to pointwise control constraints are considered. Optimal a priori error estimates are obtained for the control variable…

Optimization and Control · Mathematics 2018-09-14 Lucas Bonifacius , Konstantin Pieper , Boris Vexler

We consider an unregularized optimal control problem subject to the steady-state Navier-Stokes equations. We derive the existence of optimal solutions and prove first- and second-order optimality conditions. To approximate solutions to the…

Numerical Analysis · Mathematics 2026-05-26 Francisco Fuica , Nicolai Jork

We consider a space-time finite element method for the numerical solution of a distributed tracking-type optimal control problem subject to the heat equation with state constraints. The cost or regularization term is formulated in an…

Numerical Analysis · Mathematics 2024-10-10 Richard Löscher , Michael Reichelt , Olaf Steinbach

This work addresses the finite-horizon robust covariance control problem for discrete-time, partially observable, linear system affected by random zero mean noise and deterministic but unknown disturbances restricted to lie in what is…

Optimization and Control · Mathematics 2020-07-02 Georgios Kotsalis , Guanghui Lan , Arkadi Nemirovski

Finite element approximations of Dirichlet boundary control problems governed by parabolic PDEs on convex polygonal domains are studied in this paper. The existence of a unique solution to optimal control problems is guaranteed based on…

Optimization and Control · Mathematics 2014-10-02 Wei Gong , Michael Hinze , Zhaojie Zhou

We make some remarks on a variant of the classical Tikhonov regularization in optimal control under PDEs which allows for a certain flexibility in dealing with non-linearities and state restrictions, in the sense that differential…

Optimization and Control · Mathematics 2019-04-02 Pablo Pedregal

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…

Optimization and Control · Mathematics 2008-12-18 Radouen Ghanem

This paper is concerned with a constrained stochastic linear-quadratic optimal control problem, in which the terminal state is fixed and the initial state is constrained to lie in a stochastic linear manifold. The controllability of…

Optimization and Control · Mathematics 2019-06-11 Xiuchun Bi , Jingrui Sun , Jie Xiong

In this paper, elliptic control problems with integral constraint on the gradient of the state and box constraints on the control are considered. The optimal conditions of the problem are proved. To numerically solve the problem, we use the…

Optimization and Control · Mathematics 2018-10-05 Zixuan Chen , Xiaoliang Song , Bo Yu , Xiaotong Chen

We consider a class of parameter-dependent optimal control problems of elliptic PDEs with constraints of general type on the control variable. Applying the concept of variational discretization, [4], together with techniques from the…

Optimization and Control · Mathematics 2018-08-20 Ahmad Ahmad Ali , Michael Hinze

This article examines the Dirichlet boundary control problem governed by the Poisson equation, where the control variables are square integrable functions defined on the boundary of a two dimensional bounded, convex, polygonal domain. It…

Optimization and Control · Mathematics 2024-02-12 Sudipto Chowdhury , Divay Garg

The aim of this work is to give a broad panorama of the control properties of fractional diffusive models from a numerical analysis and simulation perspective. We do this by surveying several research results we obtained in the last years,…

Analysis of PDEs · Mathematics 2021-10-19 Umberto Biccari , Mahamadi Warma , Enrique Zuazua

We propose and analyze a new discretization technique for a linear-quadratic optimal control problem involving the fractional powers of a symmetric and uniformly elliptic second oder operator; control constraints are considered. Since these…

Numerical Analysis · Mathematics 2016-07-08 Enrique Otarola

We consider an optimal control problem $\cQ$ governed by an elliptic quasivariational inequality with unilateral constraints. The existence of optimal pairs of the problem is a well known result, see \cite{SS}, for instance. We associate to…

Optimization and Control · Mathematics 2020-05-26 Mircea Sofonea , Domingo A. Tarzia

We study the optimal control of a rate-independent system that is driven by a convex, quadratic energy. Since the associated solution mapping is non-smooth, the analysis of such control problems is challenging. In order to derive optimality…

Optimization and Control · Mathematics 2016-11-04 Ulisse Stefanelli , Gerd Wachsmuth , Daniel Wachsmuth

In this paper, we investigate optimal control problems subject to a semilinear elliptic partial differential equations. The cost functional contains a term that measures the size of the support of the control, which is the so-called…

Optimization and Control · Mathematics 2020-02-13 Eduardo Casas , Daniel Wachsmuth

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…

Numerical Analysis · Mathematics 2021-06-30 Bowen Li , Jun Zou

In this paper we investigate a priori error estimates for the space-time Galerkin finite element discretization of an optimal control problem governed by a simplified linear gradient enhanced damage model. The model equations are of a…

Numerical Analysis · Mathematics 2020-04-10 Marita Holtmannspötter , Arnd Rösch , Boris Vexler

In this paper we study we study a Dirichlet optimal control prob- lem associated with a linear elliptic equation the coefficients of which we take as controls in the class of integrable functions. The characteristic feature of this control…

Optimization and Control · Mathematics 2015-10-30 Thierry Horsin , Peter Kogut , Olivier Wilk