A splitting algorithm for constrained optimization problems with parabolic equations
DOI10.1007/s40314-023-02343-5zbMath1524.90300arXiv2302.09278MaRDI QIDQ6102418
Jiachuan Zhang, Yongle Hao, Haiming Song
Publication date: 22 June 2023
Published in: Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2302.09278
finite element methodpredictor-corrector methodparabolic equationoptimal control problemfull Jacobian decomposition method
Nonlinear programming (90C30) Numerical optimization and variational techniques (65K10) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)
Cites Work
- Unnamed Item
- Nested multigrid methods for time-periodic, parabolic optimal control problems
- Adaptive multilevel correction method for finite element approximations of elliptic optimal control problems
- Efficient time domain decomposition algorithms for parabolic PDE-constrained optimization problems
- A nonconforming finite element method for constrained optimal control problems governed by parabolic equations
- A new multigrid method for unconstrained parabolic optimal control problems
- Domain decomposition in time for PDE-constrained optimization
- Regularized Jacobi-type ADMM-methods for a class of separable convex optimization problems in Hilbert spaces
- Inexact and truncated parareal-in-time Krylov subspace methods for parabolic optimal control problems
- A posteriori error estimates of spectral method for optimal control problems governed by parabolic equations
- A new approach to improve ill-conditioned parabolic optimal control problem via time domain decomposition
- Finite Element Approximations of Parabolic Optimal Control Problems with Controls Acting on a Lower Dimensional Manifold
- Nonlinear Preconditioning Techniques for Full-Space Lagrange--Newton Solution of PDE-Constrained Optimization Problems
- A new approximation of the Schur complement in preconditioners for PDE-constrained optimization
- Indirect Multiple Shooting for Nonlinear Parabolic Optimal Control Problems with Control Constraints
- Crank--Nicolson Schemes for Optimal Control Problems with Evolution Equations
- A Posteriori Error Estimates of Mixed Methods for Quadratic Optimal Control Problems Governed by Parabolic Equations
- A Full Multigrid Method for Distributed Control Problems Constrained by Stokes Equations
- On Full Jacobian Decomposition of the Augmented Lagrangian Method for Separable Convex Programming
- A Low-Rank in Time Approach to PDE-Constrained Optimization
- Optimization with PDE Constraints
- Multigrid Methods and Sparse-Grid Collocation Techniques for Parabolic Optimal Control Problems with Random Coefficients
- A Priori Error Estimates for Space-Time Finite Element Discretization of Parabolic Optimal Control Problems Part I: Problems Without Control Constraints
- A Priori Error Estimates for Space-Time Finite Element Discretization of Parabolic Optimal Control Problems Part II: Problems with Control Constraints
- A Posteriori Error Estimates for Discontinuous Galerkin Time-Stepping Method for Optimal Control Problems Governed by Parabolic Equations
- Regularization-Robust Preconditioners for Time-Dependent PDE-Constrained Optimization Problems
- Operator Preconditioning for a Class of Inequality Constrained Optimal Control Problems
- A Symmetric Inertial Alternating Direction Method of Multipliers for Elliptic Equation Constrained Optimization Problem
- An Interface-Unfitted Finite Element Method for Elliptic Interface Optimal Control Problems
- A non-intrusive parallel-in-time approach for simultaneous optimization with unsteady PDEs
- On the Time-Domain Decomposition of Parabolic Optimal Control Problems
- Some error estimates of finite volume element method for parabolic optimal control problems
- The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent