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This paper is concerned with error estimates for the numerical approximation for affine optimal control problems subject to semilinear elliptic PDEs. To investigate the error estimates, we focus on local minimizers that satisfy certain…

Optimization and Control · Mathematics 2024-05-30 Nicolai Jork

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

Inspired by applications in optimal control of semilinear elliptic partial differential equations and physics-integrated imaging, differential equation constrained optimization problems with constituents that are only accessible through…

Optimization and Control · Mathematics 2020-08-26 Guozhi Dong , Michael Hintermueller , Kostas Papafitsoros

The first order optimality conditions of optimal control problems (OCPs) can be regarded as boundary value problems for Hamiltonian systems. Variational or symplectic discretisation methods are classically known for their excellent long…

Optimization and Control · Mathematics 2021-11-24 Christian Offen , Sina Ober-Blöbaum

We examine the minimization of a quadratic cost functional composed of the output and the final state of abstract infinite-dimensional evolution equations in view of existence of solutions and optimality conditions. While the initial value…

Optimization and Control · Mathematics 2024-12-20 Timo Reis , Manuel Schaller

We study a stochastic optimal control problem with the state constrained to a smooth, compact domain. The control influences both the drift and a possibly degenerate, control-dependent dispersion matrix, leading to a fully nonlinear,…

Optimization and Control · Mathematics 2025-08-08 Anderson O. Calixto , Bernardo Freitas Paulo da Costa , Glauco Valle

We study iterative finite element approximations for the numerical approximation of semilinear elliptic boundary value problems with monotone nonlinear reactions of subcritical growth. The focus of our contribution is on an optimal a priori…

Numerical Analysis · Mathematics 2025-08-18 Florian Spicher , Thomas P. Wihler

In this paper, we investigate optimal control problems governed by the parabolic interface equation, in which the control acts on the interface. The solution to this problem exhibits low global regularity due to the jump of the coefficient…

Numerical Analysis · Mathematics 2025-10-15 Xindan Zhang , Jianping Zhao , Yanren Hou

This work addresses an extended class of optimal control problems where a target for a system state has the form of an ellipsoid rather than a fixed, single point. As a computationally affordable method for resolving the extended problem,…

Optimization and Control · Mathematics 2025-11-14 Sungjun Eom , Gyunghoon Park

This article solves an optimal control problem arising in attitude control of a spacecraft under state and control constraints. We first derive the discrete-time attitude dynamics by employing discrete mechanics. The orientation transfer,…

Systems and Control · Computer Science 2017-11-27 Karmvir Singh Phogat , Debasish Chatterjee , Ravi Banavar

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

In this paper we propose a finite element method for solving elliptic equations with the observational Dirichlet boundary data which may subject to random noises. The method is based on the weak formulation of Lagrangian multiplier. We show…

Numerical Analysis · Mathematics 2017-02-20 Zhiming Chen , Rui Tuo , Wenlong Zhang

This paper introduces a novel approach to the optimal control of linear discrete-time systems subject to bounded disturbances. Our approach is based on the newly established duality between ellipsoidal approximations of reachable and hardly…

Systems and Control · Electrical Eng. & Systems 2024-09-20 Egor Dogadin , Alexey Peregudin , Dmitriy Shirokih

This chapter presents some numerical methods to solve problems in the fractional calculus of variations and fractional optimal control. Although there are plenty of methods available in the literature, we concentrate mainly on approximating…

Optimization and Control · Mathematics 2014-05-19 Shakoor Pooseh , Ricardo Almeida , Delfim F. M. Torres

We consider an optimal control problem governed by a class of boundary value problem with the spectral Dirichlet fractional Laplacian. Some sufficient condition for the existence of optimal processes is stated. The proof of the main result…

Analysis of PDEs · Mathematics 2017-12-29 Dorota Bors

Linear second order elliptic boundary value problems (BVP) on bounded Lipschitz domains are studied in the case of Gaussian white noise loads. Especially, Neumann and Robin BVPs are considered. The main obstacle for applying the usual…

Probability · Mathematics 2016-03-03 Sari Lasanen , Lassi Roininen , Janne M. J. Huttunen

We consider the optimal control of singular nonlinear partial differential equation which is the distributional formulation of the multiphase Stefan type free boundary problem for the general second order parabolic equation. Boundary heat…

Analysis of PDEs · Mathematics 2020-03-03 Ugur G. Abdulla , Evan Cosgrove

A priori and a posteriori error analysis of $hp$ finite element method for elliptic control problem with Robin boundary condition and boundary observation are presented. are presented. Through the Cl\'ement-type approach and the…

Numerical Analysis · Mathematics 2026-01-29 Xingyuan Lin , Xiuxiu Lin , Xuesong Chen

In this paper we study we study a Dirichlet optimal control prob- lem associated with a linear elliptic equation the coefficients of which we take as controls in the class of integrable functions. The characteristic feature of this control…

Optimization and Control · Mathematics 2015-10-30 Thierry Horsin , Peter Kogut , Olivier Wilk

We consider nonsmooth optimal control problems subject to a linear elliptic partial differential equation with homogeneous Dirichlet boundary conditions. It is well-known that local solutions satisfy the celebrated Pontryagin maximum…

Optimization and Control · Mathematics 2024-06-28 Daniel Wachsmuth