An iterative working-set method for large-scale nonconvex quadratic programming
Applied Numerical Mathematics
GALAHAD, a library of thread-safe Fortran 90 packages for large-scale nonlinear optimization
ACM Transactions on Mathematical Software (TOMS)
Preconditioning Indefinite Systems in Interior Point Methods for Optimization
Computational Optimization and Applications
Adaptive tetrahedral meshing in free-surface flow
Journal of Computational Physics
Inexact constraint preconditioners for linear systems arising in interior point methods
Computational Optimization and Applications
Computational Optimization and Applications
Using constraint preconditioners with regularized saddle-point problems
Computational Optimization and Applications
Inner solvers for interior point methods for large scale nonlinear programming
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
On the convergence of iterative methods for stabilized saddle point problems
International Journal of Computer Mathematics
Preconditioning indefinite systems in interior point methods for large scale linear optimisation
Optimization Methods & Software
Analysis of the nonlinear Uzawa algorithm for symmetric saddle point problems
International Journal of Computer Mathematics
Computational Optimization and Applications
Optimal Solvers for PDE-Constrained Optimization
SIAM Journal on Scientific Computing
A Relaxed Dimensional Factorization preconditioner for the incompressible Navier-Stokes equations
Journal of Computational Physics
On HSS-based constraint preconditioners for generalized saddle-point problems
Numerical Algorithms
SIAM Journal on Matrix Analysis and Applications
Matrix-free interior point method
Computational Optimization and Applications
Implicit solutions with consistent additive and multiplicative components
Finite Elements in Analysis and Design
A preconditioning technique for Schur complement systems arising in stochastic optimization
Computational Optimization and Applications
SIAM Journal on Scientific Computing
A Robust Two-Level Incomplete Factorization for (Navier-)Stokes Saddle Point Matrices
SIAM Journal on Matrix Analysis and Applications
All-at-once solution of time-dependent Stokes control
Journal of Computational Physics
Computational Optimization and Applications
Controlling liquids using meshes
EUROSCA'12 Proceedings of the 11th ACM SIGGRAPH / Eurographics conference on Computer Animation
Controlling liquids using meshes
Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation
On generalized parameterized inexact Uzawa method for a block two-by-two linear system
Journal of Computational and Applied Mathematics
Semi-convergence analysis of Uzawa methods for singular saddle point problems
Journal of Computational and Applied Mathematics
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We consider the application of the conjugate gradient method to the solution of large equality constrained quadratic programs arising in nonlinear optimization. Our approach is based implicitly on a reduced linear system and generates iterates in the null space of the constraints. Instead of computing a basis for this null space, we choose to work directly with the matrix of constraint gradients, computing projections into the null space by either a normal equations or an augmented system approach. Unfortunately, in practice such projections can result in significant rounding errors. We propose iterative refinement techniques, as well as an adaptive reformulation of the quadratic problem, that can greatly reduce these errors without incurring high computational overheads. Numerical results illustrating the efficacy of the proposed approaches are presented.