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We consider the bilinear optimal control of an advection-reaction-diffusion system, where the control arises as the velocity field in the advection term. Such a problem is generally challenging from both theoretical analysis and algorithmic…

Optimization and Control · Mathematics 2021-01-08 Roland Glowinski , Yongcun Song , Xiaoming Yuan , Hangrui Yue

We propose an adaptive multigrid preconditioning technology for solving linear systems arising from Discontinuous Petrov-Galerkin (DPG) discretizations. Unlike standard multigrid techniques, this preconditioner involves only trace spaces…

Numerical Analysis · Mathematics 2020-10-15 Socratis Petrides , Leszek Demkowicz

In this paper, we investigate a distributed optimal control problem for a convective viscous Cahn-Hilliard system with dynamic boundary conditions. Such systems govern phase separation processes between two phases taking place in an…

Analysis of PDEs · Mathematics 2017-09-13 Pierluigi Colli , Gianni Gilardi , Jürgen Sprekels

In this paper we apply an augmented Lagrange method to a class of semilinear elliptic optimal control problems with pointwise state constraints. We show strong convergence of subsequences of the primal variables to a local solution of the…

Optimization and Control · Mathematics 2018-10-25 Veronika Karl , Ira Neitzel , Daniel Wachsmuth

The well-posedness of a class of optimal control problems is analysed, where the state equation couples a nonlinear degenerate Fokker-Planck equation with a system of Ordinary Differential Equations (ODEs). Such problems naturally arise as…

Optimization and Control · Mathematics 2024-11-01 Francesca Anceschi , Giacomo Ascione , Daniele Castorina , Francesco Solombrino

In this paper, we are concerned with efficiently solving the sequences of regularized linear least squares problems associated with employing Tikhonov-type regularization with regularization operators designed to enforce edge recovery. An…

Numerical Analysis · Mathematics 2023-06-29 Matthias Bolten , Scott P. MacLachlan , Misha E. Kilmer

This work deals with optimal control problems as a strategy to drive bifurcating solution of nonlinear parametrized partial differential equations towards a desired branch. Indeed, for these governing equations, multiple solution…

Numerical Analysis · Mathematics 2023-08-08 Federico Pichi , Maria Strazzullo , Francesco Ballarin , Gianluigi Rozza

We solve a linear quadratic optimal control problem for sampled-data systems with stochastic delays. The delays are stochastically determined by the last few delays. The proposed optimal controller can be efficiently computed by iteratively…

Optimization and Control · Mathematics 2018-05-18 Masashi Wakaiki , Masaki Ogura , Joao P. Hespanha

We present a preconditioner for saddle point problems. The proposed preconditioner is extracted from a stationary iterative method which is convergent under a mild condition. Some properties of the preconditioner as well as the eigenvalues…

Numerical Analysis · Mathematics 2016-06-23 Davod Khojasteh Salkuyeh , Mohsen Masoudi

This paper investigates a model-free solution to the stochastic linear quadratic regulation (LQR) problem for linear discrete-time systems with both multiplicative and additive noises. We formulate the stochastic LQR problem as a nonconvex…

Optimization and Control · Mathematics 2025-12-25 Jing Guo , Xiushan Jiang , Weihai Zhang

We propose parameter-robust preconditioners for the statically condensed linear system arising from a hybridizable discontinuous Galerkin discretization of the coupled Stokes--Darcy system. The design strategy relies on first applying the…

Numerical Analysis · Mathematics 2026-04-27 Esteban Henríquez , Miroslav Kuchta , Jeonghun J. Lee , Sander Rhebergen

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

Achieving robust control and optimization in high-fidelity physics simulations is extremely challenging, especially for evolutionary systems whose solutions span vast scales across space, time, and physical variables. In conjunction with…

Optimization and Control · Mathematics 2025-05-29 Brian K. Tran , Ben S. Southworth , Hannah F. Blumhoefer , Samuel Olivier

In this paper, we study second-order necessary and sufficient optimality conditions of Karush--Kuhn--Tucker-type for locally optimal solutions in the sense of Pareto to a class of multi-objective optimal control problems with mixed…

Optimization and Control · Mathematics 2017-12-29 Bui Trong Kien , Nguyen Van Tuyen , Jen-Chih Yao

We introduce a numerical solver for the steady-state Boltzmann equation based on the symmetric Gauss-Seidel (SGS) method. To solve the nonlinear system on each grid cell derived from the SGS method, a fixed-point iteration preconditioned…

Numerical Analysis · Mathematics 2024-09-04 Zhenning Cai , Xiaoyu Dong , Jingwei Hu

The DPG method with optimal test functions for solving linear quadratic optimal control problems with control constraints is studied. We prove existence of a unique optimal solution of the nonlinear discrete problem and characterize it…

Optimization and Control · Mathematics 2023-08-21 Thomas Führer , Francisco Fuica

In this work we exploit agglomeration based $h$-multigrid preconditioners to speed-up the iterative solution of discontinuous Galerkin discretizations of the Stokes and Navier-Stokes equations. As a distinctive feature $h$-coarsened mesh…

Computational Physics · Physics 2017-09-13 Lorenzo Botti , Alessandro Colombo , Francesco Bassi

The purpose of this paper is to investigate the effects of the use of mass-lumping in the finite element discretization of the reduced first-order optimality system arising from a standard tracking-type, distributed elliptic optimal control…

Numerical Analysis · Mathematics 2023-05-01 Ulrich Langer , Richard Löscher , Olaf Steinbach , Huidong Yang

Use of the stochastic Galerkin finite element methods leads to large systems of linear equations obtained by the discretization of tensor product solution spaces along their spatial and stochastic dimensions. These systems are typically…

Numerical Analysis · Mathematics 2014-07-17 Bedřich Sousedík , Roger G. Ghanem , Eric T. Phipps

There has been a growing interest in parallel strategies for solving trajectory optimization problems. One key step in many algorithmic approaches to trajectory optimization is the solution of moderately-large and sparse linear systems.…

Optimization and Control · Mathematics 2024-03-05 Xueyi Bu , Brian Plancher