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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

In this paper we discuss the optimal control of a quasilinear parabolic state equation. Its form is leaned on the kind of problems arising for example when controlling the anisotropic Allen-Cahn equation as a model for crystal growth.…

Optimization and Control · Mathematics 2025-08-06 Luise Blank , Johannes Meisinger

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 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…

Numerical Analysis · Mathematics 2016-08-30 Alejandro Allendes , Enrique Otarola , Richard Rankin , Abner J. Salgado

In this paper we present a new steepest-descent type algorithm for convex optimization problems. Our algorithm pieces the unknown into sub-blocs of unknowns and considers a partial optimization over each sub-bloc. In quadratic optimization,…

Optimization and Control · Mathematics 2015-01-15 Mohamed Kamel Riahi

This paper is concerned with the recovery of (approximate) solutions to parabolic problems from incomplete and possibly inconsistent observational data, given on a time-space cylinder that is a strict subset of the computational domain…

Numerical Analysis · Mathematics 2021-07-13 Wolfgang Dahmen , Rob Stevenson , Jan Westerdiep

This paper first makes an attempt to investigate the partial information near optimal control of systems governed by forward-backward stochastic differential equations with observation noise under the assumption of a convex control domain.…

Optimization and Control · Mathematics 2017-08-11 Qingxin Meng , Qiuhong Shi , Maoning Tang

We study a control problem governed by a semilinear parabolic equation. The control is a measure that acts as the kernel of a possibly nonlocal time delay term and the functional includes a non-differentiable term with the measure-norm of…

Optimization and Control · Mathematics 2019-01-25 Eduardo Casas , Mariano Mateos , Fredi Tröltzsch

We consider space-time tracking optimal control problems for linear para\-bo\-lic initial boundary value problems that are given in the space-time cylinder $Q = \Omega \times (0,T)$, and that are controlled by the right-hand side…

Numerical Analysis · Mathematics 2022-06-15 Ulrich Langer , Olaf Steinbach , Huidong Yang

The paper presents the first rigorous error analysis of an unfitted finite element method for a linear parabolic problem posed on an evolving domain $\Omega(t)$ that may undergo a topological change, such as, for example, a domain…

Numerical Analysis · Mathematics 2026-01-28 Maxim A. Olshanskii , Arnold Reusken

We consider the variational discretization of a linear-quadratic optimal control problem with pointwise control and state constraints. In order to allow for a Fr\'echet smooth norm, the problem is reformulated by means of a reflexive…

Optimization and Control · Mathematics 2010-08-24 Morten Vierling

In this paper we study the conditioning of optimal control problems constrained by linear parabolic equations with Neumann boundary conditions. While we concentrate on a given end-time target function the results hold also when the target…

Numerical Analysis · Mathematics 2025-03-24 Luise Blank

We consider a control constrained parabolic optimal control problem and use variational discretization for its time semi-discretization. The state equation is treated with a Petrov-Galerkin scheme using a piecewise constant Ansatz for the…

Optimization and Control · Mathematics 2015-03-09 Nikolaus von Daniels , Michael Hinze , Morten Vierling

An adaptive direct collocation method is developed for solving optimal control problems constrained by parabolic partial differential equations. The partial differential equation is first reformulated in a variational setting, where the…

Optimization and Control · Mathematics 2026-03-18 Alexander M. Davies , Sara Pollock , Miriam E. Dennis , Anil V. Rao

We propose a semi-discrete numerical scheme and establish well-posedness of a class of parabolic systems. Such systems naturally arise while studying the optimal control of grain boundary motions. The latter is typically described using a…

Analysis of PDEs · Mathematics 2018-10-26 Harbir Antil , Ken Shirakawa , Noriaki Yamazaki

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

This work addresses an optimal control problem constrained by a degenerate kinetic equation of parabolic-hyperbolic type. Using a hypocoercivity framework we establish the well-posedness of the problem and demonstrate that the optimal…

Numerical Analysis · Mathematics 2024-12-17 Aaron Pim , Tristan Pryer , Alex Trenam

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 $\inf$--$\sup$…

Numerical Analysis · Mathematics 2023-08-03 Thomas Führer , Michael Karkulik

We discuss several optimization procedures to solve finite element approximations of linear-quadratic Dirichlet optimal control problems governed by an elliptic partial differential equation posed on a 2D or 3D Lipschitz domain. The control…

Optimization and Control · Mathematics 2019-01-25 Mariano Mateos

We consider finite element solutions to optimization problems, where the state depends on the possibly constrained control through a linear partial differential equation. Basing upon a reduced and rescaled optimality system, we derive a…

Numerical Analysis · Mathematics 2025-03-18 Fernando Gaspoz , Christian Kreuzer , Andreas Veeser , Winnifried Wollner