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Abstract
We consider the numerical solution of saddle point systems of equations
resulting from the discretization of PDEconstrained 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 subblocks of the matrix system.
resulting from the discretization of PDEconstrained 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 subblocks 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  503510 
Number of pages  8 
ISBN (Electronic)  9783319938738 
ISBN (Print)  9783319938721 
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


Computational Design Optimization of LargeScale Building Structures: Methods, Benchmarking & Applications
1/08/16 → 31/10/19
Project: Research