.png){kind=icon}
Return
A LOW-RANK MATRIX EQUATION METHOD FOR SOLVING PDE-CONSTRAINED OPTIMIZATION PROBLEMS
.png){kind=icon}
OA
AI
DOI：10.1137/20M1341210.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
PDE-constrained optimization problems arise in a broad number of applications such as hyperthermia cancer treatment and blood flow simulation. Discretization of the optimization problem and using a Lagrangian approach result in a large-scale saddle-point system, which is challenging to solve, and acquiring a full space-time solution is often infeasible. We present a new framework to efficiently compute a low-rank approximation to the solution by reformulating the KKT system into a Sylvester-like matrix equation. This matrix equation is subsequently projected onto a small subspace via an iterative rational Krylov method, and we obtain a reduced problem by imposing a Galerkin condition on its residual. In our work we discuss implementation details and dependence on the various problem parameters. Numerical experiments illustrate the performance of the new strategy also when compared to other low-rank approaches.
Keywords:
PDE-constrained optimization
matrix equation
rational Krylov subspace
Journal
IF:
2.6
Papers:
5.1K
Citations:
1.8W
Organization
Cited Papers
ShareSaveShareSaveCytotoxic and antimicrobial activities of secondary metabolites isolated from the deep-sea-derived Actinoalloteichus cyanogriseus 12A22.png)
3 Biotech
OAAI
3 BiotechIF0
OAAIShareSaveA comparative study of bridge traffic load effect using micro-simulation and Eurocode load modelsOAAI
OAAIShareSaveShareSaveShareSave
View more