Analysis and implementation of a dual algorithm for constrained optimization
Journal of Optimization Theory and Applications
Inexact and preconditioned Uzawa algorithms for saddle point problems
SIAM Journal on Numerical Analysis - Special issue: the articles in this issue are dedicated to Seymour V. Parter
Iterative solution methods
Matrix computations (3rd ed.)
Block-Triangular Preconditioners for Saddle Point Problems with a Penalty Term
SIAM Journal on Scientific Computing
Constraint Preconditioning for Indefinite Linear Systems
SIAM Journal on Matrix Analysis and Applications
Computational Optimization and Applications
Computational Optimization and Applications
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
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The implementation of the recently proposed semi-monotonic augmented Lagrangian algorithm for the solution of large convex equality constrained quadratic programming problems is considered. It is proved that if the auxiliary problems are approximately solved by the conjugate gradient method, then the algorithm finds an approximate solution of the class of problems with uniformly bounded spectrum of the Hessian matrix at O(1) matrix---vector multiplications. If applied to the class of problems with the Hessian matrices that are in addition either sufficiently sparse or can be expressed as a product of such sparse matrices, then the cost of the solution is proportional to the dimension of the problems. Theoretical results are illustrated by numerical experiments.