The rate of convergence of conjugate gradients
Numerische Mathematik
Projected gradient methods for linearly constrained problems
Mathematical Programming: Series A and B
Iterative solution methods
Iterative methods for solving linear systems
Iterative methods for solving linear systems
Duality-based domain decomposition with natural coarse-space for variational inequalities0
Journal of Computational and Applied Mathematics
Box Constrained Quadratic Programming with Proportioning and Projections
SIAM Journal on Optimization
The Primal-Dual Active Set Strategy as a Semismooth Newton Method
SIAM Journal on Optimization
Scalability and FETI based algorithm for large discretized variational inequalities
Mathematics and Computers in Simulation - MODELLING 2001 - Second IMACS conference on mathematical modelling and computational methods in mechanics, physics, biomechanics and geodynamics
Computational Optimization and Applications
A New Active Set Algorithm for Box Constrained Optimization
SIAM Journal on Optimization
Theoretically Supported Scalable FETI for Numerical Solution of Variational Inequalities
SIAM Journal on Numerical Analysis
A Primal-Dual Active Set Algorithm for Three-Dimensional Contact Problems with Coulomb Friction
SIAM Journal on Scientific Computing
Optimal Quadratic Programming Algorithms: With Applications to Variational Inequalities
Optimal Quadratic Programming Algorithms: With Applications to Variational Inequalities
A scalable FETI-DP algorithm for a coercive variational inequality
Applied Numerical Mathematics - Selected papers from the 16th Chemnitz finite element symposium 2003
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The paper resolves the problem concerning the rate of convergence of the working set based MPRGP (modified proportioning with reduced gradient projection) algorithm with a long steplength of the reduced projected gradient step. The main results of this paper are the formula for the R-linear rate of convergence of MPRGP in terms of the spectral condition number of the Hessian matrix and the proof of the finite termination property for the problems whose solution does not satisfy the strict complementarity condition. The bound on the R-linear rate of convergence of the projected gradient is also included. For shorter steplengths these results were proved earlier by Dostál and Schöberl. The efficiency of the longer steplength is illustrated by numerical experiments. The result is an important ingredient in developming scalable algorithms for numerical solution of elliptic variational inequalities and substantiates the choice of parameters that turned out to be effective in numerical experiments.