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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

This work introduces a novel, fully robust and highly-scalable, $h$-adaptive aggregated unfitted finite element method for large-scale interface elliptic problems. The new method is based on a recent distributed-memory implementation of the…

Numerical Analysis · Mathematics 2021-04-07 Eric Neiva , Santiago Badia

We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of…

Optimization and Control · Mathematics 2022-01-14 Jochen Schmid , Miltiadis Poursanidis

In this paper, a new iterative two-level algorithm is presented for solving the finite element discretization for nonsymmetric or indefinite elliptic problems. The iterative two-level algorithm uses the same coarse space as the traditional…

Numerical Analysis · Mathematics 2023-01-05 Ming Tang , Xiaoqing Xing , Ying Yang , Liuqiang Zhong

This paper deals with speeding up the convergence of a class of two-step iterative methods for solving linear systems of equations. To implement the acceleration technique, the residual norm associated with computed approximations for each…

Numerical Analysis · Mathematics 2024-04-24 Fatemeh P. A. Beik , Michele Benzi , Mehdi Najafi-Kalyani

We develop computational methods for approximating the solution of a linear multi-term matrix equation in low rank. We follow an alternating minimization framework, where the solution is represented as a product of two matrices, and…

Numerical Analysis · Mathematics 2020-06-16 Kookjin Lee , Howard C. Elman , Catherine E. Powell , Dongeun Lee

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

This paper presents the design and analysis of a Hybrid High-Order (HHO) approximation for a distributed optimal control problem governed by the Poisson equation. We propose three distinct schemes to address unconstrained control problems…

Numerical Analysis · Mathematics 2025-01-14 Gouranga Mallik , Ramesh Chandra Sau

We present an algorithm for the solution of a simultaneous space-time discretization of linear parabolic evolution equations with a symmetric differential operator in space. Building on earlier work, we recast this discretization into a…

Numerical Analysis · Mathematics 2021-09-07 Raymond van Venetië , Jan Westerdiep

Several problems in modeling and control of stochastically-driven dynamical systems can be cast as regularized semi-definite programs. We examine two such representative problems and show that they can be formulated in a similar manner. The…

Optimization and Control · Mathematics 2019-12-30 Armin Zare , Hesameddin Mohammadi , Neil K. Dhingra , Tryphon T. Georgiou , Mihailo R. Jovanović

This paper introduces a novel approach to the optimal control of linear discrete-time systems subject to bounded disturbances. Our approach is based on the newly established duality between ellipsoidal approximations of reachable and hardly…

Systems and Control · Electrical Eng. & Systems 2024-09-20 Egor Dogadin , Alexey Peregudin , Dmitriy Shirokih

This paper outlines an energy-minimization finite-element approach to the modeling of equilibrium configurations for nematic liquid crystals in the presence of internal and external electric fields. The method targets minimization of system…

Computational Physics · Physics 2014-07-14 J. H. Adler , T. J. Atherton , T. R. Benson , D. B. Emerson , S. P. MacLachlan

In this paper we investigate a priori error estimates for the space-time Galerkin finite element discretization of an optimal control problem governed by a simplified linear gradient enhanced damage model. The model equations are of a…

Numerical Analysis · Mathematics 2020-04-10 Marita Holtmannspötter , Arnd Rösch , Boris Vexler

In [1] we consider an optimal control problem subject to a semilinear elliptic PDE together with its variational discretization, where we provide a condition which allows to decide whether a solution of the necessary first order conditions…

Optimization and Control · Mathematics 2017-05-04 Ahmad Ahmad Ali , Klaus Deckelnick , Michael Hinze

We present a hierarchical computation approach for solving finite-time optimal control problems using operator splitting methods. The first split is performed over the time index and leads to as many subproblems as the length of the…

Optimization and Control · Mathematics 2013-04-09 Georgios Stathopoulos , Tamás Keviczky , Yang Wang

In this paper, we study adaptive finite element approximations in a perturbation framework, which makes use of the existing adaptive finite element analysis of a linear symmetric elliptic problem. We prove the convergence and complexity of…

Numerical Analysis · Mathematics 2010-02-05 Lianhua He , Aihui Zhou

We develop adaptive discretization algorithms for locally optimal experimental design of nonlinear prediction models. With these algorithms, we refine and improve a pertinent state-of-the-art algorithm in various respects. We establish…

Optimization and Control · Mathematics 2024-06-04 Jochen Schmid , Philipp Seufert , Michael Bortz

We develop an interpolation-based modeling framework for parameter-dependent partial differential equations arising in control, inverse problems, and uncertainty quantification. The solution is discretized in the physical domain using…

Numerical Analysis · Mathematics 2026-04-20 Erik Burman , Mats G. Larson , Karl Larsson , Jonatan Vallin

Computable estimates for the error of finite element discretisations of parabolic problems in the $L^\infty(0,T; L^2)$ norm are developed, which exhibit constant effectivities (the ratio of the estimated error to the true error) with…

Numerical Analysis · Mathematics 2018-03-09 Oliver J. Sutton

We propose a novel Galerkin discretization scheme for stochastic optimal control problems on an indefinite time horizon. The control problems are linear-quadratic in the controls, but possibly nonlinear in the state variables, and the…

Optimization and Control · Mathematics 2013-10-01 Ralf Banisch , Carsten Hartmann