PENSDP
On the solution of large-scale SDP problems by the modified barrier method using iterative solvers The limiting factors of second-order methods for large-scale semidefinite optimization are the storage and factorization of the Newton matrix. For a particular algorithm based on the modified barrier method, we propose to use iterative solvers instead of the routinely used direct factorization techniques. The preconditioned conjugate gradient method proves to be a viable alternative for problems with a large number of variables and modest size of the constrained matrix. We further propose to avoid explicit calculation of the Newton matrix either by an implicit scheme in the matrix-vector product or using a finite-difference formula. This leads to huge savings in memory requirements and, for certain problems, to further speed-up of the algorithm.
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References in zbMATH (referenced in 15 articles , 1 standard article )
Showing results 1 to 15 of 15.
Sorted by year (- Kočvara, Michal; Mohammed, Sudaba: Primal-dual interior point multigrid method for topology optimization (2016)
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- Zhao, Xin-Yuan; Sun, Defeng; Toh, Kim-Chuan: A Newton-CG augmented Lagrangian method for semidefinite programming (2010)
- Kočvara, Michal; Stingl, Michael: Erratum to: “On the solution of large-scale SDP problems by the modified barrier method using iterative solvers” (2009)
- Stingl, M.; Kočvara, M.; Leugering, G.: A sequential convex semidefinite programming algorithm with an application to multiple-load free material optimization (2009)
- Jarre, Florian; Rendl, Franz: An augmented primal-dual method for linear conic programs (2008)
- Kočvara, Michal; Stingl, Michael: On the solution of large-scale SDP problems by the modified barrier method using iterative solvers (2007)
- Kočvara, Michal; Stingl, Michael: Free material optimization for stress constraints (2007)
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- Burer, Samuel; Choi, Changhui: Computational enhancements in low-rank semidefinite programming (2006)
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