A centered projective algorithm for linear programming
Mathematics of Operations Research
Potential-reduction methods in mathematical programming
Mathematical Programming: Series A and B - Special issue: interior point methods in theory and practice
Primal-dual interior-point methods
Primal-dual interior-point methods
Matrix market: a web resource for test matrix collections
Proceedings of the IFIP TC2/WG2.5 working conference on Quality of numerical software: assessment and enhancement
Journal of Optimization Theory and Applications
Constraint Preconditioning for Indefinite Linear Systems
SIAM Journal on Matrix Analysis and Applications
The Multifrontal Solution of Indefinite Sparse Symmetric Linear
ACM Transactions on Mathematical Software (TOMS)
Krylov Subspace Methods for Saddle Point Problems with Indefinite Preconditioning
SIAM Journal on Matrix Analysis and Applications
Interior Methods for Nonlinear Optimization
SIAM Review
Preconditioning Indefinite Systems in Interior Point Methods for Optimization
Computational Optimization and Applications
Computational Optimization and Applications
Computational Optimization and Applications
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We focus on the use of adaptive stopping criteria in iterative methods for KKT systems that arise in Potential Reduction methods for quadratic programming. The aim of these criteria is to relate the accuracy in the solution of the KKT system to the quality of the current iterate, to get computational efficiency. We analyze a stopping criterion deriving from the convergence theory of inexact Potential Reduction methods and investigate the possibility of relaxing it in order to reduce as much as possible the overall computational cost. We also devise computational strategies to face a possible slowdown of convergence when an insufficient accuracy is required.