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We consider the integral definition of the fractional Laplacian and analyze a linear-quadratic optimal control problem for the so-called fractional heat equation; control constraints are also considered. We derive existence and uniqueness…

Optimization and Control · Mathematics 2020-06-24 Christian Glusa , Enrique Otarola

We consider a control-constrained parabolic optimal control problem without Tikhonov term in the tracking functional. For the numerical treatment, we use variational discretization of its Tikhonov regularization: For the state and the…

Optimization and Control · Mathematics 2017-12-08 Nikolaus von Daniels , Michael Hinze

This work presents, analyzes and tests stabilized space-time finite element methods on fully unstructured simplicial space-time meshes for the numerical solution of space-time tracking parabolic optimal control problems with the standard…

Numerical Analysis · Mathematics 2021-03-03 Ulrich Langer , Andreas Schafelner

A method is presented for the numerical solution of optimal boundary control problems governed by parabolic partial differential equations. The continuous space-time optimal control problem is transcribed into a sparse nonlinear programming…

Optimization and Control · Mathematics 2026-03-17 Alexander M. Davies , Sara Pollock , Miriam E. Dennis , Anil V. Rao

Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function and the inequality constraints are functions of the…

Optimization and Control · Mathematics 2018-02-13 Laurent Pfeiffer

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

The paper presents results about strong metric subregularity of the optimality mapping associated with the system of first-order necessary optimality conditions for a problem of optimal control of a semilinear parabolic equation. The…

Optimization and Control · Mathematics 2025-11-19 Alberto Domínguez Corella , Nicolai Jork , Vladimir M. Veliov

We consider a space-time finite element method on fully unstructured simplicial meshes for optimal sparse control of semilinear parabolic equations. The objective is a combination of a standard quadratic tracking-type functional including a…

Numerical Analysis · Mathematics 2020-04-01 Ulrich Langer , Olaf Steinbach , Fredi Tröltzsch , Huidong Yang

We present a branch-and-bound algorithm for globally solving parabolic optimal control problems with binary switches that have bounded variation and possibly need to satisfy further combinatorial constraints. More precisely, for a given…

Optimization and Control · Mathematics 2024-01-19 Christoph Buchheim , Alexandra Grütering , Christian Meyer

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

We investigate the application of a posteriori error estimates to a fractional optimal control problem with pointwise control constraints. Specifically, we address a problem in which the state equation is formulated as an integral form of…

Optimization and Control · Mathematics 2023-10-10 Fangyuan Wang , Qiming Wang , Zhaojie Zhou

We derive a-priori error estimates for the finite-element approximation of a distributed optimal control problem governed by the steady one-dimensional Burgers equation with pointwise box constraints on the control. Here the approximation…

Optimization and Control · Mathematics 2014-11-18 Pedro Martín Merino Rosero

We study linear parabolic initial-value problems in a space-time variational formulation based on fractional calculus. This formulation uses "time derivatives of order one half" on the bi-infinite time axis. We show that for linear,…

Numerical Analysis · Mathematics 2015-01-20 Stig Larsson , Christoph Schwab

We study the numerical approximation by space-time finite element methods of a multi-physics system coupling hyperbolic elastodynamics with parabolic transport and modeling poro- and thermoelasticity. The equations are rewritten as a…

Numerical Analysis · Mathematics 2023-02-14 Markus Bause , Mathias Anselmann , Uwe Köcher , Florin A. Radu

This paper is devoted to the a posteriori error analysis of multiharmonic finite element approximations to distributed optimal control problems with time-periodic state equations of parabolic type. We derive a posteriori estimates of…

Optimization and Control · Mathematics 2015-11-19 Ulrich Langer , Sergey Repin , Monika Wolfmayr

A finite element analysis of a Dirichlet boundary control problem governed by the linear parabolic equation is presented in this article. The Dirichlet control is considered in a closed and convex subset of the energy space $H^1(\Omega…

Numerical Analysis · Mathematics 2021-11-04 Thirupathi Gudi , Gouranga Mallik , Ramesh Ch. Sau

We consider variational discretization of a parabolic optimal control problem governed by space-time measure controls. For the state discretization we use a Petrov-Galerkin method employing piecewise constant states and piecewise linear and…

Optimization and Control · Mathematics 2019-11-25 Evelyn Herberg , Michael Hinze , Henrik Schumacher

We study the numerical approximation of linear-quadratic optimal control problems subject to the fractional Laplace equation with its spectral definition. We compute an approximation of the state equation using a discretization of the…

Numerical Analysis · Mathematics 2018-09-28 Stefan Dohr , Christian Kahle , Sergejs Rogovs , Piotr Swierczynski

The paper deals with an optimal control problem in a dynamical system described by a linear differential equation with the Caputo fractional derivative. The goal of control is to minimize a Bolza-type cost functional, which consists of two…

Optimization and Control · Mathematics 2019-09-25 Mikhail Gomoyunov

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