Projects per year
Abstract
We consider the numerical solution of saddle point systems of equations
resulting from the discretization of PDE-constrained optimization problems,
with additional bound constraints on the state and control variables, using an interior point method. In particular, we derive a Bramble–Pasciak Conjugate Gradient method and a tailored block triangular preconditioner which may be applied within it. Crucial to the usage of the preconditioner are carefully chosen approximations of the (1;1)-block and Schur complement of the saddle point system. To apply the inverse of the Schur complement approximation, which is computationally the most expensive part of the preconditioner, one may then utilize methods such as multigrid or domain decomposition to handle individual sub-blocks of the matrix system.
resulting from the discretization of PDE-constrained optimization problems,
with additional bound constraints on the state and control variables, using an interior point method. In particular, we derive a Bramble–Pasciak Conjugate Gradient method and a tailored block triangular preconditioner which may be applied within it. Crucial to the usage of the preconditioner are carefully chosen approximations of the (1;1)-block and Schur complement of the saddle point system. To apply the inverse of the Schur complement approximation, which is computationally the most expensive part of the preconditioner, one may then utilize methods such as multigrid or domain decomposition to handle individual sub-blocks of the matrix system.
| Original language | English |
|---|---|
| Title of host publication | Domain Decomposition Methods in Science and Engineering XXIV |
| Subtitle of host publication | DD 2017 |
| Publisher | Springer |
| Pages | 503-510 |
| Number of pages | 8 |
| ISBN (Electronic) | 978-3-319-93873-8 |
| ISBN (Print) | 978-3-319-93872-1 |
| Publication status | Published - 2018 |
Publication series
| Name | Lecture Notes in Computational Science and Engineering |
|---|---|
| Publisher | Springer |
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Dive into the research topics of 'On Block Triangular Preconditioners for the Interior Point Solution of PDE Constrained Optimization Problems'. Together they form a unique fingerprint.Projects
- 2 Finished
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Fast Solvers for Real-World PDE-Constrained Optimization
Pearson, J. (Principal Investigator)
1/08/17 → 31/05/18
Project: Research
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Computational Design Optimization of Large-Scale Building Structures: Methods, Benchmarking & Applications
Gondzio, J. (Principal Investigator)
1/08/16 → 31/10/19
Project: Research