The rate of convergence of conjugate gradients
Numerische Mathematik
Projected gradient methods for linearly constrained problems
Mathematical Programming: Series A and B
Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
A class of methods for solving large, convex quadratic programs subject to box constraints
Mathematical Programming: Series A and B
Iterative solution methods
Iterative methods for solving linear systems
Iterative methods for solving linear systems
Primal-dual interior-point methods
Primal-dual interior-point methods
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
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
A scalable FETI-DP algorithm for a coercive variational inequality
Applied Numerical Mathematics - Selected papers from the 16th Chemnitz finite element symposium 2003
A scalable FETI-DP algorithm for a coercive variational inequality
Applied Numerical Mathematics - Selected papers from the 16th Chemnitz finite element symposium 2003
FETI-based algorithms for modelling of fibrous composite materials with debonding
Mathematics and Computers in Simulation
Minimizing quadratic functions with separable quadratic constraints
Optimization Methods & Software
Aggregate dynamics for dense crowd simulation
ACM SIGGRAPH Asia 2009 papers
A scalable FETI-DP algorithm with non-penetration mortar conditions on contact interface
Journal of Computational and Applied Mathematics
Total FETI based algorithm for contact problems with additional non-linearities
Advances in Engineering Software
An efficient algorithm for a class of fused lasso problems
Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining
A scalable TFETI algorithm for two-dimensional multibody contact problems with friction
Journal of Computational and Applied Mathematics
Free-flowing granular materials with two-way solid coupling
ACM SIGGRAPH Asia 2010 papers
Structural and Multidisciplinary Optimization
Computational Optimization and Applications
Journal of Computational and Applied Mathematics
A multigrid fluid pressure solver handling separating solid boundary conditions
SCA '11 Proceedings of the 2011 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
A scalable TFETI based algorithm for 2d and 3d frictionless contact problems
LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
Mass splitting for jitter-free parallel rigid body simulation
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Mathematics and Computers in Simulation
Physics-based animation of large-scale splashing liquids
ACM Transactions on Graphics (TOG)
Computers & Mathematics with Applications
A domain decomposition method for two-body contact problems with Tresca friction
Advances in Computational Mathematics
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A new active set based algorithm is proposed that uses the conjugate gradient method to explore the face of the feasible region defined by the current iterate and the reduced gradient projection with the fixed steplength to expand the active set. The precision of approximate solutions of the auxiliary unconstrained problems is controlled by the norm of violation of the Karush-Kuhn-Tucker conditions at active constraints and the scalar product of the reduced gradient with the reduced gradient projection. The modifications were exploited to find the rate of convergence in terms of the spectral condition number of the Hessian matrix, to prove its finite termination property even for problems whose solution does not satisfy the strict complementarity condition, and to avoid any backtracking at the cost of evaluation of an upper bound for the spectral radius of the Hessian matrix. The performance of the algorithm is illustrated on solution of the inner obstacle problems. The result is an important ingredient in development of scalable algorithms for numerical solution of elliptic variational inequalities.