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We consider a numerical approximation of a linear quadratic control problem constrained by the stochastic heat equation with non-homogeneous Neumann boundary conditions. This involves a combination of distributed and boundary control, as…

Numerical Analysis · Mathematics 2021-09-28 Peter Benner , Tony Stillfjord , Christoph Trautwein

In this work, we study advection-robust Hybrid High-Order discretizations of the Oseen equations. For a given integer $k\ge 0$, the discrete velocity unknowns are vector-valued polynomials of total degree $\le k$ on mesh elements and faces,…

Numerical Analysis · Mathematics 2018-02-20 Joubine Aghili , Daniele A. Di Pietro

This paper develops and analyses numerical approximation for linear-quadratic optimal control problem governed by elliptic interface equations. We adopt variational discretization concept to discretize optimal control problem, and apply an…

Numerical Analysis · Mathematics 2018-06-04 Chao Chao Yang , Tao Wang , Xiaoping Xie

In this work we propose and analyze a novel Hybrid High-Order discretization of a class of (linear and) nonlinear elasticity models in the small deformation regime which are of common use in solid mechanics. The proposed method is valid in…

Numerical Analysis · Mathematics 2017-07-10 Michele Botti , Daniele Di Pietro , Pierre Sochala

The paper addresses an optimal control problem for a perturbed sweeping process of the rate-independent hysteresis type described by a controlled "play and stop" operator with separately controlled perturbations. This problem can be reduced…

Optimization and Control · Mathematics 2015-12-01 Tan H. Cao , Boris S. Mordukhovich

In this paper new innovative fourth order compact schemes for Robin and Neumann boundary conditions have been developed for boundary value problems of elliptic PDEs in two and three dimensions. Different from traditional finite difference…

Numerical Analysis · Mathematics 2022-06-07 Zhilin Li , Kejia Pan

We consider low-order controller design for large-scale linear time-invariant dynamical systems with inputs and outputs. Model order reduction is a popular technique, but controllers designed for reduced-order models may result in unstable…

Optimization and Control · Mathematics 2018-03-20 Peter Benner , Tim Mitchell , Michael L. Overton

We consider mixed-integer optimal control problems with combinatorial constraints that couple over time such as minimum dwell times. We analyze a lifting and decomposition approach into a mixed-integer optimal control problem without…

Optimization and Control · Mathematics 2021-04-21 Simone Göttlich , Falk M. Hante , Andreas Potschka , Lars Schewe

In the time- and frequency-limited model order reduction, a reduced-order approximation of the original high-order model is sought to ensure superior accuracy in some desired time and frequency intervals. We first consider the time-limited…

Systems and Control · Electrical Eng. & Systems 2021-01-29 Umair Zulfiqar , Victor Sreeram , Mian Ilyas Ahmad , Xin Du

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

This article is concerned with the numerical solution of convex variational problems. More precisely, we develop an iterative minimisation technique which allows for the successive enrichment of an underlying discrete approximation space in…

Numerical Analysis · Mathematics 2015-07-07 Paul Houston , Thomas P. Wihler

PDE-constrained optimal control problems require regularisation to ensure well-posedness, introducing small perturbations that make the solutions challenging to approximate accurately. We propose a finite element approach that couples both…

Numerical Analysis · Mathematics 2025-03-17 Jenny Power , Tristan Pryer

Treating optimization methods as dynamical systems can be traced back centuries ago in order to comprehend the notions and behaviors of optimization methods. Lately, this mind set has become the driving force to design new optimization…

Optimization and Control · Mathematics 2019-09-24 Arman Sharifi Kolarijani , Peyman Mohajerin Esfahani , Tamás Keviczky

Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm is proposed which can achieve approximate first-, second-…

Optimization and Control · Mathematics 2021-05-31 C. Cartis , N. I. M. Gould , Ph. L. Toint

Optimization problems with $L^1$-control cost functional subject to an elliptic partial differential equation (PDE) are considered. However, different from the finite dimensional $l^1$-regularization optimization, the resulting discretized…

Optimization and Control · Mathematics 2017-09-28 Xiaoliang Song , Bo Chen , Bo Yu

This paper considers the optimal control for hybrid systems whose trajectories transition between distinct subsystems when state-dependent constraints are satisfied. Though this class of systems is useful while modeling a variety of…

Optimization and Control · Mathematics 2018-03-21 Pengcheng Zhao , Shankar Mohan , Ram Vasudevan

In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. We consider a new unfitted finite element method…

Numerical Analysis · Mathematics 2017-06-27 Christoph Lehrenfeld , Arnold Reusken

In this paper we will consider distributed Linear-Quadratic Optimal Control Problems dealing with Advection-Diffusion PDEs for high values of the P\'eclet number. In this situation, computational instabilities occur, both for steady and…

Numerical Analysis · Mathematics 2024-05-03 Fabio Zoccolan , Maria Strazzullo , Gianluigi Rozza

This paper explores a fully discrete approximation for a nonlinear hyperbolic PDE-constrained optimization problem (P) with applications in acoustic full waveform inversion. The optimization problem is primarily complicated by the…

Numerical Analysis · Mathematics 2025-01-22 Luis Ammann , Irwin Yousept

Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…

Optimization and Control · Mathematics 2024-12-30 Tobias Breiten , Shubhaditya Burela , Philipp Schulze