.png){kind=icon}
Return
PARAOPT: A PARAREAL ALGORITHM FOR OPTIMALITY SYSTEMS
.png){kind=icon}
OA
AI
DOI：10.1137/19M1292291.png)
.png){kind=icon}
.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
The time parallel solution of optimality systems arising in PDE constrained optimization could be achieved by simply applying any time parallel algorithm, such as Parareal, to solve the forward and backward evolution problems arising in the optimization loop. We propose here a different strategy by devising directly a new time parallel algorithm, which we call ParaOpt, for the coupled forward and backward nonlinear partial differential equations. ParaOpt is inspired by the Parareal algorithm for evolution equations and thus is automatically a two-level method. We provide a detailed convergence analysis for the case of linear parabolic PDE constraints. We illustrate the performance of ParaOpt with numerical experiments for both linear and nonlinear optimality systems.
Keywords:
Parareal algorithm
optimal control
preconditioning
AI Summary
Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.
Journal
IF:
2.6
Papers:
5.1K
Citations:
1.8W
Organization
Cited Papers
.png){kind=icon}
ShareSave
ShareSaveShareSave
View more