Incomplete orthogonalization preconditioners for solving large and dense linear systems which arise from semidefinite programming

DOI10.1016/S0168-9274(01)00119-2zbMath0994.65050OpenAlexW2032229464MaRDI QIDQ1349146

Kazuhide Nakata, Shao-Liang Zhang, Kojima, Masakazu

Publication date: 21 May 2002

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0168-9274(01)00119-2

zbMATH Keywords

semidefinite programminginterior-point methodnumerical experimentsconjugate gradient methoditerative methodsincomplete orthogonalization preconditionerslarge and dense linear systems

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Semidefinite programming (90C22) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35)

Related Items (1)

On the solution of large-scale SDP problems by the modified barrier method using iterative solvers

Uses Software

• CSDP
• SDPHA
• SDPA
• SDPT3
• SDPpack
• CIMGS
• Sp

Cites Work

• Solving large and sparse linear least-squares problems by conjugate gradient algorithms
• Preconditioning techniques for nonsymmetric and indefinite linear systems
• A unified analysis for a class of long-step primal-dual path-following interior-point algorithms for semidefinite programming
• Exploiting sparsity in primal-dual interior-point methods for semidefinite programming
• Semidefinite programming relaxations for the quadratic assignment problem
• Interior-Point Methods for the Monotone Semidefinite Linear Complementarity Problem in Symmetric Matrices
• An Iterative Solution Method for Linear Systems of Which the Coefficient Matrix is a Symmetric M-Matrix
• Primal-Dual Interior-Point Methods for Semidefinite Programming: Convergence Rates, Stability and Numerical Results
• CIMGS: An Incomplete Orthogonal FactorizationPreconditioner
• Primal--Dual Path-Following Algorithms for Semidefinite Programming
• Sdpha: a Matlab implementation of homogeneous interior-point algorithms for semidefinite programming
• CSDP 2.3 user's guide
• Semidefinite Programming
• An Interior-Point Method for Semidefinite Programming
• Incomplete Methods for Solving $A^T Ax = b$
• Methods of conjugate gradients for solving linear systems
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