Robust preconditioners for finite element approximations of control-state constrained optimal control problems governed by elliptic equations
Abstract
The goal of this paper is to derive robust preconditioners for integral control-state constrained optimal control problems governed by the second order partial differential equations with linear finite element approximations. We give corresponding discretized systems of the first order necessary and sufficient optimality conditions, and get six linear algebraic systems with saddle point schemes. Furthermore, we propose efficient block preconditioners to solve the corresponding linearized algebraic systems. With respect to both mesh sizes and inherent parameters, the robustness of proposed preconditioners is proved with explicit eigenvalues of minimal polynomials. Meanwhile, we design two algorithms and choose the incomplete LU factorizations to deduce the computations. Two numerical experiments are given to depict the efficiency of our proposed preconditioners.
Related
- Constrained Mean Variance Portfolio Selection under Reflected Factor Dynamics: Stochastic Riccati Equations, Neumann Problems,and a Deep Solver
- Randomized inexact block triangular preconditioners for double saddle-point systems in PDE-constrained optimization
- Spectral analysis of a class of IRK stage preconditioners for linear wave equations
- A structure-aware construction of quantum BPX preconditioners for Q1 finite element discretizations of reaction-diffusion problems
- Parameter-robust preconditioners for a stabilized control-volume discretization of Biot's equations
BibTeX
@misc{zhang2026robust,
title = {{Robust preconditioners for finite element approximations of control-state constrained optimal control problems governed by elliptic equations}},
author = {Juan Zhang and Liang Ge and Jianwei Zhou},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01526},
eprint = {2611.01526},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01526},
}
RIS
TY - UNPB
TI - Robust preconditioners for finite element approximations of control-state constrained optimal control problems governed by elliptic equations
AU - Juan Zhang
AU - Liang Ge
AU - Jianwei Zhou
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01526
UR - https://arxiv.org/abs/2611.01526
AB - The goal of this paper is to derive robust preconditioners for integral control-state constrained optimal control problems governed by the second order partial differential equations with linear finite element approximations. We give corresponding discretized systems of the first order necessary and sufficient optimality conditions, and get six linear algebraic systems with saddle point schemes. Furthermore, we propose efficient block preconditioners to solve the corresponding linearized algebraic systems. With respect to both mesh sizes and inherent parameters, the robustness of proposed preconditioners is proved with explicit eigenvalues of minimal polynomials. Meanwhile, we design two algorithms and choose the incomplete LU factorizations to deduce the computations. Two numerical experiments are given to depict the efficiency of our proposed preconditioners.
ER -