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We derive an extension of the sequential homotopy method that allows for the application of inexact solvers for the linear (double) saddle-point systems arising in the local semismooth Newton method for the homotopy subproblems. For the…

Optimization and Control · Mathematics 2023-11-30 John W. Pearson , Andreas Potschka

We introduce a modeling framework for manipulation planning based on the formulation of the dynamics as a projected dynamical system. This method uses implicit signed distance functions and their gradients to formulate an equivalent…

Optimization and Control · Mathematics 2025-01-22 Anton Pozharskiy , Armin Nurkanović , Moritz Diehl

This paper develops a distributed model predictive control (DMPC) strategy for a class of discrete-time linear systems with consideration of globally coupled constraints. The DMPC under study is based on the dual problem concerning all…

Optimization and Control · Mathematics 2019-07-25 Yanxu Su , Yang Shi , Changyin Sun

This paper rigorously analyses preconditioners for the time-harmonic Maxwell equations with absorption, where the PDE is discretised using curl-conforming finite-element methods of fixed, arbitrary order and the preconditioner is…

Numerical Analysis · Mathematics 2020-03-23 Marcella Bonazzoli , Victorita Dolean , Ivan G. Graham , Euan A. Spence , Pierre-Henri Tournier

We explore and analyze the use of multiprecision arithmetic for several classes of Schwarz methods and preconditioners, where the approximate solution of the local problems is performed at a lower precision, i.e., with fewer digits of…

Numerical Analysis · Mathematics 2025-09-30 Michal Outrata , Daniel B. Szyld

In this paper, we propose an efficient two-level additive Schwarz method for solving large-scale eigenvalue problems arising from the finite element discretization of symmetric elliptic operators, which may compute efficiently more interior…

Numerical Analysis · Mathematics 2026-04-16 Qigang Liang , Xuejun Xu

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 a class of parameter-dependent optimal control problems of elliptic PDEs with constraints of general type on the control variable. Applying the concept of variational discretization, [4], together with techniques from the…

Optimization and Control · Mathematics 2018-08-20 Ahmad Ahmad Ali , Michael Hinze

The two-level overlapping additive Schwarz method offers a robust and scalable preconditioner for various linear systems resulting from elliptic problems. One of the key to these properties is the construction of the coarse space used to…

Numerical Analysis · Mathematics 2024-08-16 Filipe A. C. S. Alves , Alexander Heinlein , Hadi Hajibeygi

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

This paper concerns the preconditioning technique for discrete systems arising from time-harmonic Maxwell equations with absorptions, where the discrete systems are generated by N\'ed\'elec finite element methods of fixed order on meshes…

Numerical Analysis · Mathematics 2025-02-24 Ziyi Li , Qiya Hu

This paper presents a $C^0$ weak Galerkin ($C^0$-WG) method combined with an additive Schwarz preconditioner for solving optimal control problems (OCPs) governed by partial differential equations with general tracking cost functionals and…

Numerical Analysis · Mathematics 2026-04-02 SeongHee Jeong , Seulip Lee , Kening Wang

In this paper, a two-level additive Schwarz preconditioner is proposed for solving the algebraic systems resulting from the finite element approximations of space fractional partial differential equations (SFPDEs). It is shown that the…

Numerical Analysis · Mathematics 2015-01-15 Yingjun Jiang , Xuejun Xu

In this paper we study the mixed virtual element approximation to an elliptic optimal control problem with boundary observations. The objective functional of this type of optimal control problem contains the outward normal derivatives of…

Numerical Analysis · Mathematics 2023-12-19 Minghui Yang , Zhaojie Zhou

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

This paper presents a novel distributed active set method for model predictive control of linear systems. The method combines a primal active set strategy with a decentralized conjugate gradient method to solve convex quadratic programs. An…

Optimization and Control · Mathematics 2021-03-24 Gösta Stomberg , Alexander Engelmann , Timm Faulwasser

For non-preconditioned Galerkin systems, the condition number grows with the number of elements as well as the quotient of the maximal and the minimal mesh-size. Therefore, reliable and effective numerical computations, in particular on…

Numerical Analysis · Mathematics 2017-04-04 Michael Feischl , Thomas Führer , Dirk Praetorius , Ernst P. Stephan

We consider an optimal control problem subject to a semilinear elliptic PDE together with its variational discretization. We provide a condition which allows to decide whether a solution of the necessary first order conditions is a global…

Optimization and Control · Mathematics 2015-03-25 Ahmad Ahmad Ali , Klaus Deckelnick , Michael Hinze

The research of two-level overlapping Schwarz (TL-OS) method based on constrained energy minimizing coarse space is still in its infancy, and there exist some defects, e.g. mainly for second order elliptic problem and too heavy…

Numerical Analysis · Mathematics 2021-06-04 Qing Lu , Junxian Wang , Shi Shu , Jie Peng

The dynamic iteration method with a restricted additive Schwarz splitting is investigated to co-simulate linear differential algebraic equations system coming from RLC electrical circuit with linear components. We show the pure linear…

Numerical Analysis · Mathematics 2022-02-16 Helena Shourick , Damien Tromeur-Dervout , Laurent Chedot