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We analyze space-time finite element methods for the numerical solution of distributed parabolic optimal control problems with energy regularization in the Bochner space $L^2(0,T;H^{-1}(\Omega))$. By duality, the related norm can be…

Numerical Analysis · Mathematics 2020-04-22 Ulrich Langer , Olaf Steinbach , Fredi Tröltzsch , Huidong Yang

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

In this paper we consider a parabolic optimal control problem with a Dirac type control with moving point source in two space dimensions. We discretize the problem with piecewise constant functions in time and continuous piecewise linear…

Numerical Analysis · Mathematics 2018-08-17 Dmitriy Leykekhman , Boris Vexler

Optimal control of nonlinear acoustic waves is relevant in many medical ultrasound technologies, ranging from cancer therapy to targeted drug delivery, where it can help guide the precise deposition of acoustic energy. In this work, we…

Optimization and Control · Mathematics 2025-11-20 Vanja Nikolić , Belkacem Said-Houari

The paper investigates stability properties of solutions of optimal control problems for semilinear parabolic partial differential equations. H\"older or Lipschitz dependence of the optimal solution on perturbations are obtained for…

Optimization and Control · Mathematics 2025-11-18 Alberto Domínguez Corella , Nicolai Jork , Vladimir M. Veliov

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

It has been recently established that a deterministic infinite horizon discounted optimal control problem in discrete time is closely related to a certain infinite dimensional linear programming problem and its dual. In the present paper,…

Optimization and Control · Mathematics 2018-02-19 Vladimir Gaitsgory , Alex Parkinson , Ilya Shvartsman

In this work, we propose a novel diagonalization-based preconditioner for the all-at-once linear system arising from the optimal control problem of parabolic equations. The proposed preconditioner is constructed based on an…

Numerical Analysis · Mathematics 2025-07-01 Sean Y. Hon , Po Yin Fung , Xue-lei Lin

In this article a special class of nonlinear optimal control problems involving a bilinear term in the boundary condition is studied. These kind of problems arise for instance in the identification of an unknown space-dependent Robin…

Numerical Analysis · Mathematics 2024-12-20 Max Winkler

A class of time-optimal control problems governed by semilinear parabolic equations with mixed pointwise constraints and final point constraints is considered. By introducing the so-called locally optimal solution to time-optimal control…

Optimization and Control · Mathematics 2024-11-13 Huynh Khanh , Bui Trong Kien , Arnd Rösch

The purpose of this work is the development of space-time discretization schemes for phase-field optimal control problems. Specifically in the optimal control minimization problem, a tracking-type cost functional is minimized to steer the…

Optimization and Control · Mathematics 2022-09-14 Denis Khimin , Marc C. Steinbach , Thomas Wick

We introduce a domain decomposition-based nonlinear preconditioned iteration for solving nonlinear, nonsmooth elliptic optimal control problems, with a nonlinear reaction term, $L^1$ regularization and box constraints on the control…

Optimization and Control · Mathematics 2021-04-02 Gabriele Ciaramella , Felix Kwok , Georg Müller

This paper provides necessary conditions of optimality for optimal control problems with time delays in both state and control variables. Different versions of the necessary conditions cover fixed end-time problems and, under additional…

Dynamical Systems · Mathematics 2017-01-09 Andrea Boccia , Richard B. Vinter

In this paper, we investigate optimal control problems for Allen-Cahn equations with singular nonlinearities and a dynamic boundary condition involving singular nonlinearities and the Laplace-Beltrami operator. The approach covers both the…

Analysis of PDEs · Mathematics 2014-10-27 Pierluigi Colli , Jürgen Sprekels

An optimal control problem for semilinear parabolic partial differential equations is considered. The control variable appears in the leading term of the equation. Necessary conditions for optimal controls are established by the method of…

Optimization and Control · Mathematics 2010-08-20 Hongwei Lou

We study a linear-quadratic optimal control problem involving a parabolic equation with fractional diffusion and Caputo fractional time derivative of orders $s \in (0,1)$ and $\gamma \in (0,1]$, respectively. The spatial fractional…

Optimization and Control · Mathematics 2015-04-02 Harbir Antil , Enrique Otarola , Abner J. Salgado

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

In this paper we study the optimality condition for the Venttsel boundary control of a parabolic equation, that is, the state of the dynamic system is governed by a parabolic equation together with an initial condition while the control is…

Analysis of PDEs · Mathematics 2014-11-10 Yousong Luo

PDE-constrained optimization aims at finding optimal setups for partial differential equations so that relevant quantities are minimized. Including sparsity promoting terms in the formulation of such problems results in more practically…

Numerical Analysis · Mathematics 2016-11-23 Margherita Porcelli , Valeria Simoncini , Martin Stoll

A class of optimal control problems governed by linear fractional diffusion equation with control constraint is considered. We first establish some results on the existence of strong solution to the state equation and the existence of…

Optimization and Control · Mathematics 2022-11-24 Bui Trong Kien , Bui Ngoc Muoi , Ching-Feng Wen , Jen-Chih Yao