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To address the magnetization dynamics in ferromagnetic materials described by the Landau-Lifshitz-Gilbert equation under large damping parameters, a third-order accurate numerical scheme is developed by building upon a second-order method…

Numerical Analysis · Mathematics 2025-10-31 Changjian Xie , Cheng Wang

Infinite horizon open loop optimal control problems for semilinear parabolic equations are investigated. The controls are subject to a cost-functional which promotes sparsity in time. The focus is put on deriving first order optimality…

Optimization and Control · Mathematics 2021-12-14 Eduardo Casas , Karl Kunisch

We show that mean field optimal controls satisfy a first order optimality condition (at a.e. time) without any a priori requirement on their spatial regularity. This principle is obtained by a careful limit procedure of the Pontryagin…

Analysis of PDEs · Mathematics 2025-04-02 Stefano Almi , Riccardo Durastanti , Francesco Solombrino

A posteriori error estimates are an important tool to bound discretization errors in terms of computable quantities avoiding regularity conditions that are often difficult to establish. For non-linear and non-differentiable problems,…

Numerical Analysis · Mathematics 2024-06-12 Sören Bartels , Alex Kaltenbach

Nowadays, a posteriori error control methods have formed a new important part of the numerical analysis. Their purpose is to obtain computable error estimates in various norms and error indicators that show distributions of global and local…

Numerical Analysis · Mathematics 2021-11-16 Johannes Kraus , Sergey Repin

This paper is concerned with the design of optimal control for finite-dimensional control-affine nonlinear dynamical systems. We introduce an optimal control problem that specifically optimizes nonlinear observability in addition to…

Systems and Control · Computer Science 2017-08-03 Atiye Alaeddini , Kristi A. Morgansen , Mehran Mesbahi

We propose a mean-field optimal control problem for the parameter identification of a given pattern. The cost functional is based on the Wasserstein distance between the probability measures of the modeled and the desired patterns. The…

Optimization and Control · Mathematics 2021-04-08 Martin Burger , Lisa Maria Kreusser , Claudia Totzeck

We consider an optimal control problem governed by an elliptic variational inequality of the second kind. The problem is discretized by linear finite elements for the state and a variational discrete approach for the control. Based on a…

Numerical Analysis · Mathematics 2020-11-25 Christian Meyer , Monika Weymuth

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

We show how a posteriori goal oriented error estimation can be used to efficiently solve the subproblems occurring in a Model Predictive Control (MPC) algorithm. In MPC, only an initial part of a computed solution is implemented as a…

Optimization and Control · Mathematics 2022-03-02 Lars Grüne , Manuel Schaller , Anton Schiela

A posteriori error analysis is a technique to quantify the error in particular simulations of a numerical approximation method. In this article, we use such an approach to analyze how various error components propagate in certain moving…

Numerical Analysis · Mathematics 2019-09-04 Jay A. Stotsky , David M. Bortz

This paper is concerned with an optimal control problem governed by a non-smooth semilinear elliptic equation. We show that the control-to-state mapping is directionally differentiable and precisely characterize its Bouligand…

Optimization and Control · Mathematics 2018-01-29 Constantin Christof , Christian Clason , Christian Meyer , Stephan Walther

In this paper we prove necessary conditions for optimality of a stochastic control problem for a class of stochastic partial differential equations that is controlled through the boundary. This kind of problems can be interpreted as a…

Probability · Mathematics 2016-12-05 Giuseppina Guatteri

We devise an a posteriori error estimator for an affine optimal control problem subject to a semilinear elliptic PDE and control constraints. To approximate the problem, we consider a semidiscrete scheme based on the variational…

Optimization and Control · Mathematics 2025-05-08 Francisco Fuica , Nicolai Jork

In this paper, we propose a novel approximation strategy for time-dependent hyperbolic systems of conservation laws for the Euler system of gas dynamics that aims to represent the dynamics of strong interacting discontinuities. The goal of…

Numerical Analysis · Mathematics 2023-01-16 Paola Bacigaluppi , Rémi Abgrall , Svetlana Tokareva

We prove a general existence result in stochastic optimal control in discrete time where controls take values in conditional metric spaces, and depend on the current state and the information of past decisions through the evolution of a…

Optimization and Control · Mathematics 2018-12-19 Asgar Jamneshan , Michael Kupper , José Miguel Zapata

This paper studies a kind of minimal time control problems related to the exact synchronization for a controlled linear system of parabolic equations. Each problem depends on two parameters: the bound of controls and the initial state. The…

Optimization and Control · Mathematics 2018-03-02 Lijuan Wang , Qishu Yan

We apply innovative mathematical tools coming from optimal control theory to improve theoretical and experimental techniques in Magnetic Resonance Imaging (MRI). This approach allows us to explore and to experimentally reach the physical…

Quantum Physics · Physics 2017-09-11 E. Van-Reeth , H. Ratiney , M. Lapert , S. J. Glaser , D. Sugny

In this paper we present and analyze a weighted residual a posteriori error estimate for an optimal control problem. The problem involves a nondifferentiable cost functional, a state equation with an integral fractional Laplacian, and…

Numerical Analysis · Mathematics 2023-09-18 Fangyuan Wang , Qiming Wang , Zhaojie Zhou

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