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ON MUTUAL IMPACT OF NUMERICAL LINEAR ALGEBRA AND LARGESCALE OPTIMIZATION WITH FOCUS ON INTERIOR POINT METHODS
, 2008
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A Relaxed Dimensional Factorization Preconditioner for the Incompressible NavierStokes Equations
, 2010
"... In this paper we introduce a Relaxed Dimensional Factorization (RDF) preconditioner for saddle point problems. Properties of the preconditioned matrix are analyzed and compared with those of the closely related Dimensional Splitting (DS) preconditioner recently introduced by Benzi and Guo in [8]. Nu ..."
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Cited by 9 (3 self)
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In this paper we introduce a Relaxed Dimensional Factorization (RDF) preconditioner for saddle point problems. Properties of the preconditioned matrix are analyzed and compared with those of the closely related Dimensional Splitting (DS) preconditioner recently introduced by Benzi and Guo in [8]. Numerical results for a variety of finite element discretizations of both steady and unsteady incompressible flow problems indicate very good behavior of the RDF preconditioner with respect to both mesh size and viscosity.
A preconditioning technique for Schur complement systems arising in stochastic optimization
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Some Preconditioning Techniques for Saddle Point Problems
"... Saddle point problems arise frequently in many applications in science and engineering, including constrained optimization, mixed finite element formulations of partial differential equations, circuit analysis, and so forth. Indeed the formulation of most problems with constraints gives rise to sadd ..."
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Cited by 5 (1 self)
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Saddle point problems arise frequently in many applications in science and engineering, including constrained optimization, mixed finite element formulations of partial differential equations, circuit analysis, and so forth. Indeed the formulation of most problems with constraints gives rise to saddle point systems. This paper provides a
Constraintstyle preconditioners for regularized saddle point problems
, 2006
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A PRECONDITIONER FOR LINEAR SYSTEMS ARISING FROM INTERIOR POINT OPTIMIZATION METHODS
"... Abstract. We explore a preconditioning technique applied to the problem of solving linear systems arising from primaldual interior point algorithms in linear and quadratic programming. The preconditioner has the attractive property of improved eigenvalue clustering with increased illconditioning of ..."
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Abstract. We explore a preconditioning technique applied to the problem of solving linear systems arising from primaldual interior point algorithms in linear and quadratic programming. The preconditioner has the attractive property of improved eigenvalue clustering with increased illconditioning of the (1,1) block of the saddle point matrix. It fits well into the optimization framework since the interior point iterates yield increasingly illconditioned linear systems as the solution is approached. We analyze the spectral characteristics of the preconditioner, utilizing projections onto the null space of the constraint matrix, and demonstrate performance on problems from the NETLIB and CUTEr test suites. The numerical experiments include results based on inexact inner iterations. Key words. block preconditioners, saddle point systems, primaldual interior point methods, augmentation
A class of nonsymmetric preconditioners for saddle point problems
 Scientific Computing and Computational Mathematics, Stanford University, of Saddle Point Problems 77
, 2004
"... Abstract. For iterative solution of saddle point problems, a nonsymmetric preconditioning is studied which, with respect to the upperleft block of the system matrix, can be seen as a variant of SSOR. An idealized situation where the SSOR is taken with respect to the skewsymmetric part plus the dia ..."
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Cited by 3 (1 self)
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Abstract. For iterative solution of saddle point problems, a nonsymmetric preconditioning is studied which, with respect to the upperleft block of the system matrix, can be seen as a variant of SSOR. An idealized situation where the SSOR is taken with respect to the skewsymmetric part plus the diagonal part of the upperleft block is analyzed in detail. Since action of the preconditioner involves solution of a Schur complement system, an inexact form of the preconditioner can be of interest. This results in an innerouter iterative process. Numerical experiments with solution of linearized NavierStokes equations demonstrate efficiency of the new preconditioner, especially when the leftupper block is far from symmetric.
Augmentation preconditioning for saddle point systems
, 2006
"... We investigate a preconditioning technique applied to the problem of solving linear systems arising from primaldual interior point algorithms in linear and quadratic programming. The preconditioner has the attractive property of improved eigenvalue clustering with increased illconditioning of the ..."
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Cited by 1 (1 self)
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We investigate a preconditioning technique applied to the problem of solving linear systems arising from primaldual interior point algorithms in linear and quadratic programming. The preconditioner has the attractive property of improved eigenvalue clustering with increased illconditioning of the (1, 1) block of the saddle point matrix. We demonstrate performance of the preconditioner on problems from the NETLIB and CUTEr test suites. The numerical experiments include results based on inexact inner iterations, and comparisons of the proposed techniques with constraint preconditioners. Approximations to the preconditioner are considered for systems with simple (1, 1) blocks. The preconditioning approach is also extended to deal with stabilized systems. We show that for stabilized saddle point systems a minimum residual Krylov method will converge in just two iterations. iii Contents Abstract.................................... ii