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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

This paper continues the investigations from [7] and is concerned with the derivation of first-order conditions for a control constrained optimization problem governed by a non-smooth elliptic PDE. The control enters the state equation not…

Optimization and Control · Mathematics 2025-02-11 Livia Betz

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 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

This paper is dedicated to the stability analysis of the optimal solutions of a control problem associated with a semilinear elliptic equation. The linear differential operator of the equation is neither monotone nor coercive due to the…

Optimization and Control · Mathematics 2025-11-20 Eduardo Casas , Alberto Domínguez Corella , Nicolai Jork

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

An optimal control problem driven by an ordinary differential equation under continuous state constraints is considered in this study. From an operational point of view, we introduce a discrete state constraints optimal control problem and…

Optimization and Control · Mathematics 2018-12-04 Shuzhen Yang

We consider a linear-quadratic optimization problem with pointwise bounds on the state for which the constraint is given by the Laplace-Beltrami equation (to have uniqueness we add an lower order term) on a two-dimensional surface . By…

Optimization and Control · Mathematics 2016-06-10 Ahmad Ahmad Ali , Michael Hinze , Heiko Kröner

We investigate $C^1$ finite element methods for one dimensional elliptic distributed optimal control problems with pointwise constraints on the derivative of the state formulated as fourth order variational inequalities for the state…

Numerical Analysis · Mathematics 2020-06-29 Susanne C. Brenner , Li-Yeng Sung , Winnifried Wollner

Motivated by various applications, this article develops the notion of boundary control for Maxwell's equations in the frequency domain. Surface curl is shown to be the appropriate regularization in order for the optimal control problem to…

Optimization and Control · Mathematics 2022-10-03 Harbir Antil , Hugo Díaz

We consider an abstract framework for the numerical solution of optimal control problems (OCPs) subject to partial differential equations (PDEs). Examples include not only the distributed control of elliptic PDEs such as the Poisson…

Numerical Analysis · Mathematics 2025-05-27 Ulrich Langer , Richard Löscher , Olaf Steinbach , Huidong Yang

We consider some boundary value tracking optimal control problem constrained by a Neumann boundary value problem for some elliptic partial differential equation where the control acts as right-hand side. This optimal control problem can be…

Numerical Analysis · Mathematics 2026-03-12 Ulrich Langer , Richard Löscher , Olaf Steinbach , Huidong Yang

In this paper we study the optimal control of a class of semilinear elliptic partial differential equations which have nonlinear constituents that are only accessible by data and are approximated by nonsmooth ReLU neural networks. The…

Optimization and Control · Mathematics 2022-10-24 Guozhi Dong , Michael Hintermüller , Kostas Papafitsoros , Kathrin Völkner

In this paper we derive a necessary optimality condition for a local optimal solution of some control problems. These optimal control problems are governed by a semi-linear Vettsel boundary value problem of a linear elliptic equation. The…

Analysis of PDEs · Mathematics 2009-04-08 Yousong Luo

We investigate the numerical approximation of an elliptic optimal control problem which involves a nonconvex local regularization of the $L^q$-quasinorm penalization (with $q\in(0,1)$) in the cost function. Our approach is based on the…

Optimization and Control · Mathematics 2022-09-26 Pedro Merino , Alexander Nenjer

In this paper we establish well posedness of the Neumann problem with boundary data in $L^2$ or the Sobolev space $\dot W^2_{-1}$, in the half space, for linear elliptic differential operators with coefficients that are constant in the…

Analysis of PDEs · Mathematics 2017-03-22 Ariel Barton , Steve Hofmann , Svitlana Mayboroda

In this paper, an optimal control problem governed by a class of p-Laplacian elliptic equations is studied. In particular, as no monotonicity assumption is assumed on the nonlinear term, the state equation may admit several solutions for…

Optimization and Control · Mathematics 2019-08-28 Hongwei Lou , Shu Luan

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

A numerical study of an optimal control formulation for a shape optimization problem governed by an elliptic variational inequality is performed. The shape optimization problem is reformulated as a boundary control problem in a fixed…

Optimization and Control · Mathematics 2018-01-22 Raino A. E. Mäkinen

We consider a linear-quadratic pde constrained optimal control problem on an evolving surface with pointwise state constraints. We reformulate the optimization problem on a fixed surface and approximate the reformulated problem by a…

Optimization and Control · Mathematics 2016-04-27 Michael Hinze , Heiko Kröner