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Related papers: Optimal control of elliptic PDEs at points

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This work is concerned with the optimal control problems governed by a 1D wave equation with variable coefficients and the control spaces $\mathcal M_T$ of either measure-valued functions $L_{w^*}^2(I,\mathcal M(\Omega))$ or vector measures…

Numerical Analysis · Mathematics 2026-01-05 Philip Trautmann , Boris Vexler , Alexander Zlotnik

This papers shows the convergence of optimal control problems where the constraint function is discretised by a particle method. In particular, we investigate the viscous Burgers equation in the whole space $\mathbb R$ by using…

Optimization and Control · Mathematics 2013-10-01 Jan Marburger , Rene Pinnau

This paper is concerned with the discretization error analysis of semilinear Neumann boundary control problems in polygonal domains with pointwise inequality constraints on the control. The approximations of the control are piecewise…

Numerical Analysis · Mathematics 2015-05-12 Johannes Pfefferer , Klaus Krumbiegel

We analyze an optimal control problem with pointwise tracking for a fractional semilinear elliptic partial differential equation. The diffusion is characterized by the spectral fractional Laplacian $(-\Delta)^s$ with $s \in (1/2,1)$, a…

Optimization and Control · Mathematics 2026-04-17 Enrique Otarola , Abner J. Salgado

In this paper, we derive explicit second-order necessary and sufficient optimality conditions of a local minimizer to an optimal control problem for a quasilinear second-order partial differential equation with a piecewise smooth but not…

Optimization and Control · Mathematics 2023-09-13 Christian Clason , Vu Huu Nhu , Arnd Rösch

In this paper, problems of optimal control are considered where in the objective function, in addition to the control cost there is a tracking term that measures the distance to a desired stationary state. The tracking term is given by some…

Optimization and Control · Mathematics 2020-06-15 Martin Gugat , Michael Schuster , Enrique Zuazua

Optimal Control Problems consist on the optimisation of an objective functional subjected to a set of Ordinary Differential Equations. In this work, we consider the effects on the stability of the numerical solution when this optimisation…

Optimization and Control · Mathematics 2024-01-09 Ashutosh Bijalwan , Jose J Muñoz

We consider control-constrained linear-quadratic optimal control problems on evolving surfaces. In order to formulate well-posed problems, we prove existence and uniqueness of weak solutions for the state equation, in the sense of…

Optimization and Control · Mathematics 2015-03-19 Morten Vierling

In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. Recently a new unfitted finite element method…

Numerical Analysis · Mathematics 2017-09-01 Christoph Lehrenfeld , Arnold Reusken

This paper is concerned with the development of weak Galerkin (WG) finite element method for optimal control problems governed by second order elliptic partial differential equations (PDEs). It is advantageous to use discontinuous finite…

Numerical Analysis · Mathematics 2023-10-03 Chunmei Wang , Junping Wang , Shangyou Zhang

This work establishes a general stochastic maximum principle for partially observed optimal control of semi-linear stochastic partial differential equations in a nonconvex control domain. The state evolves in a Hilbert space driven by a…

Optimization and Control · Mathematics 2025-04-22 Yanzhao Cao , Hongjiang Qian , George Yin

This paper considers the finite element approximation to parabolic optimal control problems with measure data in a nonconvex polygonal domain. Such problems usually possess low regularity in the state variable due to the presence of measure…

Numerical Analysis · Mathematics 2024-03-12 Pratibha Shakya

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

The paper is concerned with an optimal control problem governed by the rate-independent system of quasi-static perfect elasto-plasticity. The objective is optimize the displacement field in the domain occupied by the body by means of…

Optimization and Control · Mathematics 2020-03-24 Christian Meyer , Stephan Walther

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

In this paper we consider optimal control problems where the control variable is a potential and the state equation is an elliptic partial differential equation of a Schr\"odinger type, governed by the Laplace operator. The cost functional…

Optimization and Control · Mathematics 2023-02-07 Giuseppe Buttazzo , Juan Casado_Díaz , Faustino Maestre

We present a new parallel computational framework for the efficient solution of a class of $L^2$/$L^1$-regularized optimal control problems governed by semi-linear elliptic partial differential equations (PDEs). The main difficulty in…

Optimization and Control · Mathematics 2025-08-20 Gabriele Ciaramella , Michael Kartmann , Georg Müller

This paper investigates numerical methods for solving stochastic linear quadratic (SLQ) optimal control problems governed by stochastic partial differential equations (SPDEs). Two distinct approaches, the open-loop and closed-loop ones, are…

Optimization and Control · Mathematics 2024-11-19 Andreas Prohl , Yanqing Wang

In this paper, we present and analyze an interior penalty discontinuous Galerkin method for the distributed elliptic optimal control problems. It is based on a reconstructed discontinuous approximation which admits arbitrarily high-order…

Numerical Analysis · Mathematics 2026-01-05 Ruo Li , Haoyang Liu , Jun Yin

We devise and analyze a reliable and efficient a posteriori error estimator for a semilinear control-constrained optimal control problem in two and three dimensional Lipschitz, but not necessarily convex, polytopal domains. We consider a…

Numerical Analysis · Mathematics 2019-11-22 Alejandro Allendes , Francisco Fuica , Enrique Otarola , Daniel Quero