Preconditioning the augmented Lagrangian method for instationary mean field games with diffusion

Abstract : We discuss the application of the augmented Lagrangian method to the convex optimization problem of instationary variational mean field games with diffusion. The problem is first discretized with space-time tensor product piecewise polynomial bases. This leads to a sequence of linear problems posed on the space-time cylinder that are second order in the temporal variable and fourth order in the spatial variable. To solve these large linear problems with the preconditioned conjugate gradients method we propose a preconditioner that is based on a temporal transformation coupled with a spatial multigrid. This preconditioner is thus based on standard components and is particularly suitable for parallel computation. It is conditionally parameter-robust in the sense that the condition number of the preconditioned system is low for sufficiently fine temporal discretizations. Numerical examples illustrate the method.
Complete list of metadatas

Cited literature [26 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01301282
Contributor : Roman Andreev <>
Submitted on : Monday, May 1, 2017 - 7:48:52 PM
Last modification on : Friday, May 24, 2019 - 5:22:33 PM
Long-term archiving on : Wednesday, August 2, 2017 - 12:32:20 PM

File

ALG2MFG_HAL_20170501.pdf
Files produced by the author(s)

Licence


Distributed under a Creative Commons Attribution 4.0 International License

Identifiers

  • HAL Id : hal-01301282, version 2

Citation

Roman Andreev. Preconditioning the augmented Lagrangian method for instationary mean field games with diffusion. 2017. ⟨hal-01301282v2⟩

Share

Metrics

Record views

1164

Files downloads

290