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We consider linear model reduction in both the control and state variables for unconstrained linear-quadratic optimal control problems subject to time-varying parabolic PDEs. The first-order optimality condition for a state-space reduced…

Optimization and Control · Mathematics 2025-10-17 Michael Kartmann , Stefan Volkwein

This article deals with error estimates for the finite element approximation of variational normal derivatives and, as a consequence, error estimates for the finite element approximation of Dirichlet boundary control problems with energy…

Numerical Analysis · Mathematics 2018-08-06 Max Winkler

A continuous optimal control problem governed by an elliptic variational inequality was considered in Boukrouche-Tarzia, Comput. Optim. Appl., 53 (2012), 375-392 where the control variable is the internal energy $g$. It was proved the…

Numerical Analysis · Mathematics 2015-05-18 Mariela Olguín , Domingo A. Tarzia

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

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

Traditional finite element approaches are well-known to introduce spurious oscillations when applied to advection-dominated problems. We explore alleviation of this issue from the perspective of a generalized finite element formulation,…

Numerical Analysis · Mathematics 2021-10-04 Troy Shilt , Patrick O'Hara , Jack J. McNamara

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

We consider control constrained optimal control problems governed by parameterized stationary Maxwell's system with the Gauss's law. The parameters enter through dielectric, magnetic permeability, and charge density. Moreover, the parameter…

Optimization and Control · Mathematics 2020-04-20 Harbir Antil , Tran Nhan Tam Quyen

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

The numerical approximation of an inverse problem subject to the convection--diffusion equation when diffusion dominates is studied. We derive Carleman estimates that are on a form suitable for use in numerical analysis and with explicit…

Numerical Analysis · Mathematics 2020-06-25 Erik Burman , Mihai Nechita , Lauri Oksanen

We analyze a bilinear optimal control problem for the Stokes--Brinkman equations: the control variable enters the state equations as a coefficient. In two- and three-dimensional Lipschitz domains, we perform a complete continuous analysis…

Numerical Analysis · Mathematics 2025-10-22 Alejandro Allendes , Gilberto Campaña , Enrique Otarola

We consider an unregularized optimal control problem subject to the steady-state Navier-Stokes equations. We derive the existence of optimal solutions and prove first- and second-order optimality conditions. To approximate solutions to the…

Numerical Analysis · Mathematics 2026-05-26 Francisco Fuica , Nicolai Jork

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 develop the max-plus finite element method to solve finite horizon deterministic optimal control problems. This method, that we introduced in a previous work, relies on a max-plus variational formulation, and exploits the properties of…

Optimization and Control · Mathematics 2016-11-18 Marianne Akian , Stephane Gaubert , Asma Lakhoua

In this paper, we consider a class of time-optimal control problems governed by linear parabolic equations with mixed control-state constraints and end-point constraints, and without Tikhonov regularization term in the objective function.…

Optimization and Control · Mathematics 2025-09-04 Huynh Khanh , Bui Trong Kien

This work is concerned with quasi-optimal a-priori finite element error estimates for the obstacle problem in the $L^2$-norm. The discrete approximations are introduced as solutions to a finite element discretization of an accordingly…

Numerical Analysis · Mathematics 2018-11-26 Dominik Hafemeyer , Christian Kahle , Johannes Pfefferer

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 propose and analyze a posteriori error estimators for an optimal control problem that involves an elliptic partial differential equation as state equation and a control variable that enters the state equation as a coefficient; pointwise…

Optimization and Control · Mathematics 2022-03-31 Francisco Fuica , Enrique Otarola

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 design and analyze solution techniques for a linear-quadratic optimal control problem involving the integral fractional Laplacian. We derive existence and uniqueness results, first order optimality conditions, and regularity estimates…

Optimization and Control · Mathematics 2020-10-09 Marta D'Elia , Christian Glusa , Enrique Otarola