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We derive existence results and first order necessary optimality conditions for optimal control problems governed by quasilinear parabolic PDEs with a class of first order nonlinearities that include for instance quadratic gradient terms.…

Optimization and Control · Mathematics 2025-07-03 Lucas Bonifacius , Fabian Hoppe , Hannes Meinlschmidt , Ira Neitzel

This paper introduces the notion of state constraints for optimal control problems governed by fractional elliptic PDEs of order $s \in (0,1)$. There are several mathematical tools that are developed during the process to study this…

Optimization and Control · Mathematics 2019-06-04 Harbir Antil , Deepanshu Verma , Mahamadi Warma

This paper proposes a $C^{0}$ (non-Lagrange) primal finite element approximation of the linear elliptic equations in non-divergence form with oblique boundary conditions in planar, curved domains. As an extension of [Calcolo, 58 (2022), No.…

Numerical Analysis · Mathematics 2022-06-28 Guangwei Gao , Shuonan Wu

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

This paper establishes the optimal $H^1$-norm error estimate for a nonstandard finite element method for approximating $H^2$ strong solutions of second order linear elliptic PDEs in non-divergence form with continuous coefficients. To…

Numerical Analysis · Mathematics 2019-10-01 Xiaobing Feng , Stefan Schnake

This paper considers the problem of determining an optimal control action based on observed data. We formulate the problem assuming that the system can be modelled by a nonlinear state-space model, but where the model parameters, state and…

Optimization and Control · Mathematics 2021-07-02 Johannes N. Hendriks , James R. Z. Holdsworth , Adrian G. Wills , Thomas B. Schon , Brett Ninness

We propose an a posteriori error estimator for a sparse optimal control problem: the control variable lies in the space of regular Borel measures. We consider a solution technique that relies on the discretization of the control variable as…

Numerical Analysis · Mathematics 2018-06-14 Francisco Fuica , Enrique Otarola , Abner J. Salgado

In this paper, error estimates are presented for a certain class of optimal control problems with elliptic PDE-constraints. It is assumed that in the cost functional the state is measured in terms of the energy norm generated by the state…

Numerical Analysis · Mathematics 2014-10-31 Olli Mali

The present paper represents a continuation of our previous one. There, a continuous dependence result for the solution of an elliptic variational-hemivariational inequality was obtained and then used to prove the existence of optimal pairs…

Analysis of PDEs · Mathematics 2019-12-25 Yi-bin Xiao , Mircea Sofonea

We derive a posteriori error estimators for an optimal control problem governed by a convection-reaction-diffusion equation; control constraints are also considered. We consider a family of low-order stabilized finite element methods to…

Numerical Analysis · Mathematics 2017-04-24 Alejandro Allendes , Enrique Otarola , Richard Rankin

In this paper, we consider a special class of nonlinear optimal control problems, where the control variables are box-constrained and the objective functional is strongly convex corresponding to control variables and separable with respect…

Optimization and Control · Mathematics 2022-01-20 Hailing Wang , Di Wu , Changjun Yu

We are concerned with a class of second order quasilinear elliptic equations driven by a nonhomogeneous differential operator introduced by C.A. Stuart and whose study is motivated by models in Nonlinear Optics. We establish sufficient…

Analysis of PDEs · Mathematics 2022-01-04 Louis Jeanjean , Vicentiu D. Radulescu

This paper is dedicated to the investigation of a new numerical method to approximate the optimal stopping problem for a discrete-time continuous state space Markov chain under partial observations. It is based on a two-step discretization…

Optimization and Control · Mathematics 2016-02-16 Benoîte de Saporta , François Dufour , Christophe Nivot

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

This paper aims at solving an optimal control problem governed by an anisotropic Allen-Cahn equation numerically. Therefore we first prove the Fr\'echet differentiability of an in time discretized parabolic control problem under certain…

Optimization and Control · Mathematics 2024-08-12 Luise Blank , Johannes Meisinger

We devise a posteriori error estimators for quasi-optimal nonconforming finite element methods approximating symmetric elliptic problems of second and fourth order. These estimators are defined for all source terms that are admissible to…

Numerical Analysis · Mathematics 2025-02-05 Christian Kreuzer , Matthias Rott , Andreas Veeser , Pietro Zanotti

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 introduce a domain decomposition-based nonlinear preconditioned iteration for solving nonlinear, nonsmooth elliptic optimal control problems, with a nonlinear reaction term, $L^1$ regularization and box constraints on the control…

Optimization and Control · Mathematics 2021-04-02 Gabriele Ciaramella , Felix Kwok , Georg Müller

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…

Numerical Analysis · Mathematics 2014-11-19 C. Brett , A. S. Dedner , C. M. Elliott

We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…

Numerical Analysis · Mathematics 2019-10-23 Philipp A. Guth , Vesa Kaarnioja , Frances Y. Kuo , Claudia Schillings , Ian H. Sloan
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