GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Mathematical Programming: Series A and B
On the identification of local minimizers in inertia-controlling methods for quadratic programming
SIAM Journal on Matrix Analysis and Applications
Preconditioners for indefinite systems arising in optimization
SIAM Journal on Matrix Analysis and Applications
Computational results of an interior point algorithm for large scale linear programming
Mathematical Programming: Series A and B - Special issue on interior point methods for linear programming: theory and practice
An interior point method for quadratic programs based on conjugate projected gradients
Computational Optimization and Applications
Fast iterative solution of stabilised Stokes systems part II: using general block preconditioners
SIAM Journal on Numerical Analysis
Software for simplified Lanczos and QMR algorithms
Applied Numerical Mathematics - Special issue on iterative methods for linear equations
Matrix computations (3rd ed.)
Stability of Augmented System Factorizations in Interior-Point Methods
SIAM Journal on Matrix Analysis and Applications
Journal of Optimization Theory and Applications
Accurate Symmetric Indefinite Linear Equation Solvers
SIAM Journal on Matrix Analysis and Applications
An Interior-Point Algorithm for Nonconvex Nonlinear Programming
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part II
Incomplete Cholesky Factorizations with Limited Memory
SIAM Journal on Scientific Computing
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)
Symbiosis between linear algebra and optimization
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
On the Solution of Equality Constrained Quadratic Programming Problems Arising in Optimization
SIAM Journal on Scientific Computing
Krylov Subspace Methods for Saddle Point Problems with Indefinite Preconditioning
SIAM Journal on Matrix Analysis and Applications
Interior Methods for Nonlinear Optimization
SIAM Review
Ill-Conditioning and Computational Error in Interior Methods for Nonlinear Programming
SIAM Journal on Optimization
A Revised Modified Cholesky Factorization Algorithm
SIAM Journal on Optimization
Solving the Trust-Region Subproblem using the Lanczos Method
SIAM Journal on Optimization
Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
Object-oriented software for quadratic programming
ACM Transactions on Mathematical Software (TOMS)
SQP Methods for Large-Scale Nonlinear Programming
Proceedings of the 19th IFIP TC7 Conference on System Modelling and Optimization: Methods, Theory and Applications
Inertia-controlling factorizations for optimization algorithms
Applied Numerical Mathematics
Preconditioning Indefinite Systems in Interior Point Methods for Optimization
Computational Optimization and Applications
Mathematical Programming: Series A and B
Approximate Factorization Constraint Preconditioners for Saddle-Point Matrices
SIAM Journal on Scientific Computing
Implicit-Factorization Preconditioning and Iterative Solvers for Regularized Saddle-Point Systems
SIAM Journal on Matrix Analysis and Applications
Inexact constraint preconditioners for linear systems arising in interior point methods
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
Iterative Solution of Augmented Systems Arising in Interior Methods
SIAM Journal on Optimization
Constraint-Style Preconditioners for Regularized Saddle Point Problems
SIAM Journal on Matrix Analysis and Applications
Parallel inexact constraint preconditioners for saddle point problems
Euro-Par'11 Proceedings of the 17th international conference on Parallel processing - Volume Part II
Matrix-free interior point method
Computational Optimization and Applications
A preconditioning technique for Schur complement systems arising in stochastic optimization
Computational Optimization and Applications
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The solution of KKT systems is ubiquitous in optimization methods and often dominates the computation time, especially when large-scale problems are considered. Thus, the effective implementation of such methods is highly dependent on the availability of effective linear algebra algorithms and software, that are able, in turn, to take into account specific needs of optimization. In this paper we discuss the mutual impact of linear algebra and optimization, focusing on interior point methods and on the iterative solution of the KKT system. Three critical issues are addressed: preconditioning, termination control for the inner iterations, and inertia control.