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A new approach to solving two-point boundary value problems for a wave equation is developed. This new approach exploits the principle of stationary action to reformulate and solve such problems in the framework of optimal control. In…

Optimization and Control · Mathematics 2017-11-13 Peter M. Dower , William M. McEneaney

In this paper, we study numerical approximations for optimal control of a class of stochastic partial differential equations with partial observations. The system state evolves in a Hilbert space, whereas observations are given in…

Optimization and Control · Mathematics 2025-04-02 Feng Bao , Yanzhao Cao , Hongjiang Qian

We consider a class of (ill-posed) optimal control problems in which a distributed vector-valued control is enforced to pointwise take values in a finite set $\mathcal{M}\subset\mathbb{R}^m$. After convex relaxation, one obtains a…

Optimization and Control · Mathematics 2018-06-28 Christian Clason , Carla Tameling , Benedikt Wirth

A dual control problem is presented for the optimal stochastic control of a system governed by partial differential equations. Relationships between the optimal values of the original and the dual problems are investigated and two duality…

Optimization and Control · Mathematics 2017-05-03 Shinji Tanimoto

We present a novel energy-based numerical analysis of semilinear diffusion-reaction boundary value problems. Based on a suitable variational setting, the proposed computational scheme can be seen as an energy minimisation approach. More…

Numerical Analysis · Mathematics 2022-02-16 Mario Amrein , Pascal Heid , Thomas P. Wihler

The paper deals with a stochastic Galerkin approximation of elliptic Dirichlet boundary control problems with random input data. The expectation of a tracking cost functional with the deterministic constrained control is minimized. Error…

Optimization and Control · Mathematics 2025-06-16 Max Winkler , Hamdullah Yücel

In the present paper we investigate the inverse problem of identifying simultaneously the diffusion matrix, source term and boundary condition as well as the state in the Neumann boundary value problem for an elliptic partial differential…

Numerical Analysis · Mathematics 2018-01-18 Tran Nhan Tam Quyen

We present a method for the numerical approximation of distributed optimal control problems constrained by parabolic partial differential equations. We complement the first-order optimality condition by a recently developed space-time…

Numerical Analysis · Mathematics 2022-08-23 Thomas Führer , Michael Karkulik

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

A numerical procedure providing guaranteed two-sided bounds on the effective coefficients of elliptic partial differential operators is presented. The upper bounds are obtained in a standard manner through the variational formulation of the…

Numerical Analysis · Mathematics 2023-07-24 Liya Gaynutdinova , Martin Ladecký , Aleš Nekvinda , Ivana Pultarová , Jan Zeman

We consider a distributed optimal control problem subject to a parabolic evolution equation as constraint. The control will be considered in the energy norm of the anisotropic Sobolev space $[H_{0;,0}^{1,1/2}(Q)]^\ast$, such that the state…

Numerical Analysis · Mathematics 2025-02-14 Richard Löscher , Michael Reichelt , Olaf Steinbach

An optimal control problem subject to an elliptic obstacle problem is studied. We obtain a numerical approximation of this problem by discretising the PDE obtained via a Moreau--Yosida type penalisation. For the resulting discrete control…

Optimization and Control · Mathematics 2018-10-22 Ahmad Ahmad Ali , Klaus Deckelnick , Michael Hinze

We adopt the integral definition of the fractional Laplace operator and study an optimal control problem on Lipschitz domains that involves a fractional elliptic partial differential equation (PDE) as state equation and a control variable…

Numerical Analysis · Mathematics 2024-02-14 Francisco Bersetche , Francisco Fuica , Enrique Otarola , Daniel Quero

This paper deals with the numerical computation of boundary null controls for the 1D wave equation with a potential. The goal is to compute an approximation of controls that drive the solution from a prescribed initial state to zero at a…

Optimization and Control · Mathematics 2015-02-03 Nicolae Cîndea , Enrique Fernandez-Cara , Arnaud Munch

We consider a control-constrained parabolic optimal control problem without Tikhonov term in the tracking functional. For the numerical treatment, we use variational discretization of its Tikhonov regularization: For the state and the…

Optimization and Control · Mathematics 2017-12-08 Nikolaus von Daniels , Michael Hinze

This article provides quasi-optimal a priori error estimates for an optimal control problem constrained by an elliptic obstacle problem where the finite element discretization is carried out using the symmetric interior penalty…

Numerical Analysis · Mathematics 2023-12-21 Harbir Antil , Rohit Khandelwal , Umarkhon Rakhimov

We introduce the tensor numerical method for solving optimal control problems that are constrained by fractional 2D and 3D elliptic operators with variable coefficients. We solve the governing equation for the control function which…

Numerical Analysis · Mathematics 2020-07-07 Britta Schmitt , Boris N. Khoromskij , Venera Khoromskaia , Volker Schulz

We study a discretization technique for the parabolic fractional obstacle problem in bounded domains. The fractional Laplacian is realized as the Dirichlet-to-Neumann map for a nonuniformly elliptic equation posed on a semi-infinite…

Numerical Analysis · Mathematics 2015-07-09 Enrique Otarola , Abner J. Salgado

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 propose and analyze reliable and efficient a posteriori error estimators for an optimal control problem that involves a nondifferentiable cost functional, the Poisson problem as state equation and control constraints. To approximate the…

Numerical Analysis · Mathematics 2019-01-14 Alejandro Allendes , Francisco Fuica , Enrique Otárola