English
Related papers

Related papers: Parareal in time intermediate targets methods for …

200 papers

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

The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite…

Optimization and Control · Mathematics 2014-08-20 Vladimir Gaitsgory , Sergei Rossomakhine

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

This article proposes modifications of the Parareal algorithm for its application to higher index differential algebraic equations (DAEs). It is based on the idea of applying the algorithm to only the differential components of the equation…

Numerical Analysis · Mathematics 2022-10-05 Idoia Cortes Garcia , Iryna Kulchytska-Ruchka , Sebastian Schöps

We present a method for the numerical approximation of distributed optimal control problems constrained by parabolic partial differential equations. We complement the first-order optimality condition by a recently developed space-time…

Numerical Analysis · Mathematics 2022-08-23 Thomas Führer , Michael Karkulik

We present new Dirichlet-Neumann and Neumann-Dirichlet algorithms with a time domain decomposition applied to unconstrained parabolic optimal control problems. After a spatial semi-discretization, we use the Lagrange multiplier approach to…

Numerical Analysis · Mathematics 2023-08-25 Martin Jakob Gander , Liu-Di Lu

In this paper, we introduce a novel pseudospectral method for the numerical solution of optimal control problems governed by a parabolic distributed parameter system. The infinite-dimensional optimal control problem is reduced into a…

Optimization and Control · Mathematics 2023-03-06 Kareem T. Elgindy

Discrete variational methods show excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative procedure for the solution of discrete variational equations for boundary value…

Optimization and Control · Mathematics 2022-06-22 Sebastián J. Ferraro , David Martín de Diego , Rodrigo Takuro Sato Martín de Almagro

This paper presents a novel parallel-in-time algorithm able to compute time-periodic solutions of problems where the period is not given. Exploiting the idea of the multiple shooting method, the proposed approach calculates the initial…

Numerical Analysis · Mathematics 2020-07-08 Iryna Kulchytska-Ruchka , Sebastian Schöps

We derive energy-norm a posteriori error bounds for an Euler time-stepping method combined with various spatial discontinuous Galerkin schemes for linear parabolic problems. For accessibility, we address first the spatially semidiscrete…

Numerical Analysis · Mathematics 2011-04-06 Emmanuil H. Georgoulis , Omar Lakkis , Juha M. Virtanen

A geometric approach to kinematics in control theory is illustrated. A non-linear control system is derived for the problem and the Pontryagin maximum principle is used to find the time-optimal trajectories of the Parallel navigation. The…

Optimization and Control · Mathematics 2011-01-11 M. Rafie-Rad

Optimal control of bilinear systems has been a well-studied subject in the area of mathematical control. However, techniques for solving emerging optimal control problems involving an ensemble of structurally identical bilinear systems are…

Optimization and Control · Mathematics 2016-01-14 Shuo Wang , Jr-Shin Li

We present the conditions under which the time-optimal control problem for a nonlinear non-autonomous linearizable system can be solved by the method of successive approximations, at each step of which a power Markov moment min-problem is…

Optimization and Control · Mathematics 2022-03-17 Katerina V. Sklyar , Svetlana Yu. Ignatovich

We consider the usage of parallel-in-time algorithms of the Parareal and multigrid-reduction-in-time (MGRIT) methodologies for the parallel-in-time solution of the eddy current problem. Via application of these methods to a two-dimensional…

Numerical Analysis · Mathematics 2018-11-01 Stephanie Friedhoff , Jens Hahne , Iryna Kulchytska-Ruchka , Sebastian Schöps

Asking for the optimal protocol of an external control parameter that minimizes the mean work required to drive a nano-scale system from one equilibrium state to another in finite time, Schmiedl and Seifert ({\it Phys. Rev. Lett.} {\bf 98},…

Statistical Mechanics · Physics 2008-04-14 Holger Then , Andreas Engel

In this paper we present explicit bounds for optimal control in a Lagrange problem without end-point constraints. The approach we use is due to Gamkrelidze and is based on the equivalence of the Lagrange problem and a time-optimal problem…

Optimization and Control · Mathematics 2018-01-03 Miguel Oliveira , Georgi Smirnov

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

This paper presents a mathematical formulation to perform temporal parallelisation of continuous-time optimal control problems, which can be solved via the Hamilton--Jacobi--Bellman (HJB) equation. We divide the time interval of the control…

Optimization and Control · Mathematics 2024-12-18 Simo Särkkä , Ángel F. García-Fernández

We present a time-parallelization method that enables to accelerate the computation of quantum optimal control algorithms. We show that this approach is approximately fully efficient when based on a gradient method as optimization solver:…

Optimization and Control · Mathematics 2016-05-04 Mohamed-Kamel Riahi , Julien Salomon , S. J. Glaser , D Sugny

This work concentrates on a class of optimal control problems for semilinear parabolic equations subject to control constraint of the form $\|u(t)\|_{L^1(\Omega)} \le \gamma$ for $t \in (0,T)$. This limits the total control that can be…

Optimization and Control · Mathematics 2021-12-03 Eduardo Casas , Karl Kunisch