Preconditioning Indefinite Systems in Interior Point Methods for Optimization
Computational Optimization and Applications
Stopping criteria for inner iterations in inexact potential reduction methods: a computational study
Computational Optimization and Applications
Using constraint preconditioners with regularized saddle-point problems
Computational Optimization and Applications
Computational Optimization and Applications
Limiting accuracy of segregated solution methods for nonsymmetric saddle point problems
Journal of Computational and Applied Mathematics
Mixed Constraint Preconditioners for the iterative solution of FE coupled consolidation equations
Journal of Computational Physics
Preconditioning indefinite systems in interior point methods for large scale linear optimisation
Optimization Methods & Software
Computational Optimization and Applications
Preconditioning Saddle-Point Systems with Applications in Optimization
SIAM Journal on Scientific Computing
Riemannian Newton Method for the Multivariate Eigenvalue Problem
SIAM Journal on Matrix Analysis and Applications
MINRES-QLP: A Krylov Subspace Method for Indefinite or Singular Symmetric Systems
SIAM Journal on Scientific Computing
Matrix-free interior point method
Computational Optimization and Applications
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In this paper we analyze the null-space projection (constraint) indefinite preconditioner applied to the solution of large-scale saddle point problems. Nonsymmetric Krylov subspace solvers are analyzed; moreover, it is shown that the behavior of short-term recurrence methods can be related to the behavior of preconditioned conjugate gradient method (PCG). Theoretical properties of PCG are studied in detail and simple procedures for correcting possible misconvergence are proposed. The numerical behavior of the scheme on a real application problem is discussed and the maximum attainable accuracy of the approximate solution computed in finite precision arithmetic is estimated.